Adaptations for gmkin

Address winbuilder check problems, update check log, update of static docs
author: Johannes Ranke <jranke@uni-bremen.de> 2019-07-08 18:12:21 +0200
committer: Johannes Ranke <jranke@uni-bremen.de> 2019-07-09 09:10:02 +0200
commit: e0bef15657df1d6cade99cc3f6d8b07fa35792fe (patch)
tree: 7d050ac3b25e37a952a1f4efa46263980fbe502b /docs/articles
parent: 67d032fb345f8e0afc7628d7525da5b7f0a98f79 (diff)
27 files changed, 912 insertions, 695 deletions
diff --git a/docs/articles/FOCUS_D.html b/docs/articles/FOCUS_D.html
index 341c7e7d..00c3cabe 100644
--- a/docs/articles/FOCUS_D.html
+++ b/docs/articles/FOCUS_D.html
@@ -88,7 +88,7 @@
       <h1>Example evaluation of FOCUS Example Dataset D</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2019-07-05</h4>
+            <h4 class="date">2019-07-09</h4>
       
       
       <div class="hidden name"><code>FOCUS_D.Rmd</code></div>
@@ -156,18 +156,20 @@
 ##             "d_m1 = + k_parent_m1 * parent - k_m1_sink * m1"</code></pre>
 <p>We do the fitting without progress report (<code>quiet = TRUE</code>).</p>
 <div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" title="1">fit &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(SFO_SFO, FOCUS_<span class="dv">2006</span>_D, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<pre><code>## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
+## value of zero were removed from the data</code></pre>
 <p>A plot of the fit including a residual plot for both observed variables is obtained using the <code>plot_sep</code> method for <code>mkinfit</code> objects, which shows separate graphs for all compounds and their residuals.</p>
-<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" title="1"><span class="kw"><a href="../reference/plot.mkinfit.html">plot_sep</a></span>(fit, <span class="dt">lpos =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"topright"</span>, <span class="st">"bottomright"</span>))</a></code></pre></div>
+<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" title="1"><span class="kw"><a href="../reference/plot.mkinfit.html">plot_sep</a></span>(fit, <span class="dt">lpos =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"topright"</span>, <span class="st">"bottomright"</span>))</a></code></pre></div>
 <p><img src="FOCUS_D_files/figure-html/plot-1.png" width="768"></p>
 <p>Confidence intervals for the parameter estimates are obtained using the <code>mkinparplot</code> function.</p>
-<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" title="1"><span class="kw"><a href="../reference/mkinparplot.html">mkinparplot</a></span>(fit)</a></code></pre></div>
+<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" title="1"><span class="kw"><a href="../reference/mkinparplot.html">mkinparplot</a></span>(fit)</a></code></pre></div>
 <p><img src="FOCUS_D_files/figure-html/plot_2-1.png" width="768"></p>
 <p>A comprehensive report of the results is obtained using the <code>summary</code> method for <code>mkinfit</code> objects.</p>
-<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(fit)</a></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.48.1 
+<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb11-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(fit)</a></code></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.49.6 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Fri Jul  5 15:52:50 2019 
-## Date of summary: Fri Jul  5 15:52:50 2019 
+## Date of fit:     Tue Jul  9 09:00:18 2019 
+## Date of summary: Tue Jul  9 09:00:18 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent - k_parent_m1 * parent
@@ -175,16 +177,19 @@
 ## 
 ## Model predictions using solution type deSolve 
 ## 
-## Fitted with method Port using 153 model solutions performed in 0.63 s
+## Fitted using 389 model solutions performed in 1.003 s
 ## 
-## Weighting: none
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##                  value   type
-## parent_0      100.7500  state
-## k_parent_sink   0.1000 deparm
-## k_parent_m1     0.1001 deparm
-## k_m1_sink       0.1002 deparm
+##                    value   type
+## parent_0      100.750000  state
+## k_parent_sink   0.100000 deparm
+## k_parent_m1     0.100100 deparm
+## k_m1_sink       0.100200 deparm
+## sigma           3.125504  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##                        value lower upper
@@ -192,6 +197,7 @@
 ## log_k_parent_sink  -2.302585  -Inf   Inf
 ## log_k_parent_m1    -2.301586  -Inf   Inf
 ## log_k_m1_sink      -2.300587  -Inf   Inf
+## sigma               3.125504     0   Inf
 ## 
 ## Fixed parameter values:
 ##      value  type
@@ -199,31 +205,38 @@
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##                   Estimate Std. Error  Lower   Upper
-## parent_0            99.600    1.61400 96.330 102.900
-## log_k_parent_sink   -3.038    0.07826 -3.197  -2.879
-## log_k_parent_m1     -2.980    0.04124 -3.064  -2.897
-## log_k_m1_sink       -5.248    0.13610 -5.523  -4.972
+## parent_0            99.600    1.57000 96.400 102.800
+## log_k_parent_sink   -3.038    0.07626 -3.193  -2.883
+## log_k_parent_m1     -2.980    0.04033 -3.062  -2.898
+## log_k_m1_sink       -5.248    0.13320 -5.518  -4.977
+## sigma                3.126    0.35850  2.396   3.855
 ## 
 ## Parameter correlation:
-##                   parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
-## parent_0           1.00000            0.6075        -0.06625       -0.1701
-## log_k_parent_sink  0.60752            1.0000        -0.08740       -0.6253
-## log_k_parent_m1   -0.06625           -0.0874         1.00000        0.4716
-## log_k_m1_sink     -0.17006           -0.6253         0.47164        1.0000
-## 
-## Residual standard error: 3.211 on 36 degrees of freedom
+##                     parent_0 log_k_parent_sink log_k_parent_m1
+## parent_0           1.000e+00         6.067e-01      -6.372e-02
+## log_k_parent_sink  6.067e-01         1.000e+00      -8.550e-02
+## log_k_parent_m1   -6.372e-02        -8.550e-02       1.000e+00
+## log_k_m1_sink     -1.688e-01        -6.252e-01       4.731e-01
+## sigma              1.164e-09        -8.908e-10       1.652e-08
+##                   log_k_m1_sink      sigma
+## parent_0             -1.688e-01  1.164e-09
+## log_k_parent_sink    -6.252e-01 -8.908e-10
+## log_k_parent_m1       4.731e-01  1.652e-08
+## log_k_m1_sink         1.000e+00 -1.340e-10
+## sigma                -1.340e-10  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
 ##                Estimate t value    Pr(&gt;t)     Lower     Upper
-## parent_0      99.600000  61.720 2.024e-38 96.330000 1.029e+02
-## k_parent_sink  0.047920  12.780 3.050e-15  0.040890 5.616e-02
-## k_parent_m1    0.050780  24.250 3.407e-24  0.046700 5.521e-02
-## k_m1_sink      0.005261   7.349 5.758e-09  0.003992 6.933e-03
+## parent_0      99.600000  63.430 2.298e-36 96.400000 1.028e+02
+## k_parent_sink  0.047920  13.110 6.126e-15  0.041030 5.596e-02
+## k_parent_m1    0.050780  24.800 3.269e-23  0.046780 5.512e-02
+## k_m1_sink      0.005261   7.510 6.165e-09  0.004012 6.898e-03
+## sigma          3.126000   8.718 2.235e-10  2.396000 3.855e+00
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   6.398       4 15
 ## parent     6.827       3  6
@@ -260,8 +273,6 @@
 ##    50   parent     0.63   0.71624 -8.624e-02
 ##    75   parent     0.05   0.06074 -1.074e-02
 ##    75   parent     0.06   0.06074 -7.382e-04
-##     0       m1     0.00   0.00000  0.000e+00
-##     0       m1     0.00   0.00000  0.000e+00
 ##     1       m1     4.84   4.80296  3.704e-02
 ##     1       m1     5.64   4.80296  8.370e-01
 ##     3       m1    12.91  13.02400 -1.140e-01
@@ -276,8 +287,8 @@
 ##    35       m1    37.95  43.31312 -5.363e+00
 ##    50       m1    41.19  41.21831 -2.831e-02
 ##    50       m1    40.01  41.21831 -1.208e+00
-##    75       m1    40.09  36.44704  3.643e+00
-##    75       m1    33.85  36.44704 -2.597e+00
+##    75       m1    40.09  36.44703  3.643e+00
+##    75       m1    33.85  36.44703 -2.597e+00
 ##   100       m1    31.04  31.98163 -9.416e-01
 ##   100       m1    33.13  31.98163  1.148e+00
 ##   120       m1    25.15  28.78984 -3.640e+00
diff --git a/docs/articles/FOCUS_D_files/figure-html/plot-1.png b/docs/articles/FOCUS_D_files/figure-html/plot-1.png
index c0c6e567..fc1142ab 100644
--- a/docs/articles/FOCUS_D_files/figure-html/plot-1.png
+++ b/docs/articles/FOCUS_D_files/figure-html/plot-1.png
diff --git a/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png b/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png
index 9caac2b9..97c61a16 100644
--- a/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png
+++ b/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png
diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html
index 73ea645a..779635cd 100644
--- a/docs/articles/FOCUS_L.html
+++ b/docs/articles/FOCUS_L.html
@@ -88,7 +88,7 @@
       <h1>Example evaluation of FOCUS Laboratory Data L1 to L3</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2019-07-05</h4>
+            <h4 class="date">2019-07-09</h4>
       
       
       <div class="hidden name"><code>FOCUS_L.Rmd</code></div>
@@ -112,54 +112,59 @@
 <p>Since mkin version 0.9-32 (July 2014), we can use shorthand notation like <code>"SFO"</code> for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.</p>
 <div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" title="1">m.L1.SFO &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"SFO"</span>, FOCUS_<span class="dv">2006</span>_L1_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
 <a class="sourceLine" id="cb2-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.L1.SFO)</a></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.48.1 
+<pre><code>## mkin version used for fitting:    0.9.49.6 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Fri Jul  5 15:52:52 2019 
-## Date of summary: Fri Jul  5 15:52:52 2019 
+## Date of fit:     Tue Jul  9 09:00:20 2019 
+## Date of summary: Tue Jul  9 09:00:20 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 37 model solutions performed in 0.084 s
+## Fitted using 133 model solutions performed in 0.282 s
 ## 
-## Weighting: none
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##               value   type
-## parent_0      89.85  state
-## k_parent_sink  0.10 deparm
+##                   value   type
+## parent_0      89.850000  state
+## k_parent_sink  0.100000 deparm
+## sigma          2.779827  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##                       value lower upper
 ## parent_0          89.850000  -Inf   Inf
 ## log_k_parent_sink -2.302585  -Inf   Inf
+## sigma              2.779827     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##                   Estimate Std. Error  Lower  Upper
-## parent_0            92.470    1.36800 89.570 95.370
-## log_k_parent_sink   -2.347    0.04057 -2.433 -2.261
+## parent_0            92.470    1.28200 89.740 95.200
+## log_k_parent_sink   -2.347    0.03763 -2.428 -2.267
+## sigma                2.780    0.46330  1.792  3.767
 ## 
 ## Parameter correlation:
-##                   parent_0 log_k_parent_sink
-## parent_0            1.0000            0.6248
-## log_k_parent_sink   0.6248            1.0000
-## 
-## Residual standard error: 2.948 on 16 degrees of freedom
+##                     parent_0 log_k_parent_sink      sigma
+## parent_0           1.000e+00         6.186e-01 -1.712e-09
+## log_k_parent_sink  6.186e-01         1.000e+00 -3.237e-09
+## sigma             -1.712e-09        -3.237e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
 ##               Estimate t value    Pr(&gt;t)    Lower   Upper
-## parent_0      92.47000   67.58 2.170e-21 89.57000 95.3700
-## k_parent_sink  0.09561   24.65 1.867e-14  0.08773  0.1042
+## parent_0      92.47000   72.13 8.824e-21 89.74000 95.2000
+## k_parent_sink  0.09561   26.57 2.487e-14  0.08824  0.1036
+## sigma          2.78000    6.00 1.216e-05  1.79200  3.7670
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   3.424       2  7
 ## parent     3.424       2  7
@@ -200,18 +205,22 @@
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-5-1.png" width="576"></p>
 <p>For comparison, the FOMC model is fitted as well, and the <span class="math inline">\(\chi^2\)</span> error level is checked.</p>
 <div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" title="1">m.L1.FOMC &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"FOMC"</span>, FOCUS_<span class="dv">2006</span>_L1_mkin, <span class="dt">quiet=</span><span class="ot">TRUE</span>)</a></code></pre></div>
-<pre><code>## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation by method Port did not converge:
+<pre><code>## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
 ## false convergence (8)</code></pre>
 <div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L1.FOMC, <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>, <span class="dt">main =</span> <span class="st">"FOCUS L1 - FOMC"</span>)</a></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-6-1.png" width="576"></p>
 <div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.L1.FOMC, <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.48.1 
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
+## finite result is doubtful</code></pre>
+<pre><code>## mkin version used for fitting:    0.9.49.6 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Fri Jul  5 15:52:54 2019 
-## Date of summary: Fri Jul  5 15:52:54 2019 
+## Date of fit:     Tue Jul  9 09:00:22 2019 
+## Date of summary: Tue Jul  9 09:00:22 2019 
 ## 
 ## 
-## Warning: Optimisation by method Port did not converge:
+## Warning: Optimisation did not converge:
 ## false convergence (8) 
 ## 
 ## 
@@ -220,49 +229,54 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 741 model solutions performed in 1.637 s
+## Fitted using 899 model solutions performed in 1.881 s
 ## 
-## Weighting: none
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 89.85  state
-## alpha     1.00 deparm
-## beta     10.00 deparm
+##              value   type
+## parent_0 89.850000  state
+## alpha     1.000000 deparm
+## beta     10.000000 deparm
+## sigma     2.779871  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##               value lower upper
 ## parent_0  89.850000  -Inf   Inf
 ## log_alpha  0.000000  -Inf   Inf
 ## log_beta   2.302585  -Inf   Inf
+## sigma      2.779871     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error    Lower   Upper
-## parent_0     92.47      1.454    89.37   95.57
-## log_alpha    10.58   1164.000 -2471.00 2492.00
-## log_beta     12.93   1164.000 -2469.00 2495.00
+##           Estimate Std. Error  Lower  Upper
+## parent_0     92.47     1.2800 89.730 95.220
+## log_alpha    10.58        NaN    NaN    NaN
+## log_beta     12.93        NaN    NaN    NaN
+## sigma         2.78     0.4507  1.813  3.747
 ## 
 ## Parameter correlation:
-##           parent_0 log_alpha log_beta
-## parent_0    1.0000    0.2361   0.2361
-## log_alpha   0.2361    1.0000   1.0000
-## log_beta    0.2361    1.0000   1.0000
-## 
-## Residual standard error: 3.045 on 15 degrees of freedom
+##           parent_0 log_alpha log_beta   sigma
+## parent_0   1.00000       NaN      NaN 0.01452
+## log_alpha      NaN         1      NaN     NaN
+## log_beta       NaN       NaN        1     NaN
+## sigma      0.01452       NaN      NaN 1.00000
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##           Estimate  t value    Pr(&gt;t) Lower Upper
-## parent_0     92.47 65.32000 3.886e-20 89.37 95.57
-## alpha     39440.00  0.01639 4.936e-01  0.00   Inf
-## beta     412500.00  0.01639 4.936e-01  0.00   Inf
+##           Estimate  t value    Pr(&gt;t)  Lower  Upper
+## parent_0     92.47 72.13000 1.052e-19 89.730 95.220
+## alpha     39440.00  0.02397 4.906e-01     NA     NA
+## beta     412500.00  0.02397 4.906e-01     NA     NA
+## sigma         2.78  6.00000 1.628e-05  1.813  3.747
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   3.619       3  6
 ## parent     3.619       3  6
@@ -278,19 +292,19 @@
 <h1 class="hasAnchor">
 <a href="#laboratory-data-l2" class="anchor"></a>Laboratory Data L2</h1>
 <p>The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:</p>
-<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb11-1" title="1">FOCUS_<span class="dv">2006</span>_L2 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a>
-<a class="sourceLine" id="cb11-2" title="2">  <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/rep">rep</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">1</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">28</span>), <span class="dt">each =</span> <span class="dv">2</span>),</a>
-<a class="sourceLine" id="cb11-3" title="3">  <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">96.1</span>, <span class="fl">91.8</span>, <span class="fl">41.4</span>, <span class="fl">38.7</span>,</a>
-<a class="sourceLine" id="cb11-4" title="4">             <span class="fl">19.3</span>, <span class="fl">22.3</span>, <span class="fl">4.6</span>, <span class="fl">4.6</span>,</a>
-<a class="sourceLine" id="cb11-5" title="5">             <span class="fl">2.6</span>, <span class="fl">1.2</span>, <span class="fl">0.3</span>, <span class="fl">0.6</span>))</a>
-<a class="sourceLine" id="cb11-6" title="6">FOCUS_<span class="dv">2006</span>_L2_mkin &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L2)</a></code></pre></div>
+<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb14-1" title="1">FOCUS_<span class="dv">2006</span>_L2 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a>
+<a class="sourceLine" id="cb14-2" title="2">  <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/rep">rep</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">1</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">28</span>), <span class="dt">each =</span> <span class="dv">2</span>),</a>
+<a class="sourceLine" id="cb14-3" title="3">  <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">96.1</span>, <span class="fl">91.8</span>, <span class="fl">41.4</span>, <span class="fl">38.7</span>,</a>
+<a class="sourceLine" id="cb14-4" title="4">             <span class="fl">19.3</span>, <span class="fl">22.3</span>, <span class="fl">4.6</span>, <span class="fl">4.6</span>,</a>
+<a class="sourceLine" id="cb14-5" title="5">             <span class="fl">2.6</span>, <span class="fl">1.2</span>, <span class="fl">0.3</span>, <span class="fl">0.6</span>))</a>
+<a class="sourceLine" id="cb14-6" title="6">FOCUS_<span class="dv">2006</span>_L2_mkin &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L2)</a></code></pre></div>
 <div id="sfo-fit-for-l2" class="section level2">
 <h2 class="hasAnchor">
 <a href="#sfo-fit-for-l2" class="anchor"></a>SFO fit for L2</h2>
 <p>Again, the SFO model is fitted and the result is plotted. The residual plot can be obtained simply by adding the argument <code>show_residuals</code> to the plot command.</p>
-<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb12-1" title="1">m.L2.SFO &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"SFO"</span>, FOCUS_<span class="dv">2006</span>_L2_mkin, <span class="dt">quiet=</span><span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb12-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L2.SFO, <span class="dt">show_residuals =</span> <span class="ot">TRUE</span>, <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>,</a>
-<a class="sourceLine" id="cb12-3" title="3">     <span class="dt">main =</span> <span class="st">"FOCUS L2 - SFO"</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb15-1" title="1">m.L2.SFO &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"SFO"</span>, FOCUS_<span class="dv">2006</span>_L2_mkin, <span class="dt">quiet=</span><span class="ot">TRUE</span>)</a>
+<a class="sourceLine" id="cb15-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L2.SFO, <span class="dt">show_residuals =</span> <span class="ot">TRUE</span>, <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>,</a>
+<a class="sourceLine" id="cb15-3" title="3">     <span class="dt">main =</span> <span class="st">"FOCUS L2 - SFO"</span>)</a></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-8-1.png" width="672"></p>
 <p>The <span class="math inline">\(\chi^2\)</span> error level of 14% suggests that the model does not fit very well. This is also obvious from the plots of the fit, in which we have included the residual plot.</p>
 <p>In the FOCUS kinetics report, it is stated that there is no apparent systematic error observed from the residual plot up to the measured DT90 (approximately at day 5), and there is an underestimation beyond that point.</p>
@@ -300,64 +314,69 @@
 <h2 class="hasAnchor">
 <a href="#fomc-fit-for-l2" class="anchor"></a>FOMC fit for L2</h2>
 <p>For comparison, the FOMC model is fitted as well, and the <span class="math inline">\(\chi^2\)</span> error level is checked.</p>
-<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1">m.L2.FOMC &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"FOMC"</span>, FOCUS_<span class="dv">2006</span>_L2_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb13-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L2.FOMC, <span class="dt">show_residuals =</span> <span class="ot">TRUE</span>,</a>
-<a class="sourceLine" id="cb13-3" title="3">     <span class="dt">main =</span> <span class="st">"FOCUS L2 - FOMC"</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb16-1" title="1">m.L2.FOMC &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"FOMC"</span>, FOCUS_<span class="dv">2006</span>_L2_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
+<a class="sourceLine" id="cb16-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L2.FOMC, <span class="dt">show_residuals =</span> <span class="ot">TRUE</span>,</a>
+<a class="sourceLine" id="cb16-3" title="3">     <span class="dt">main =</span> <span class="st">"FOCUS L2 - FOMC"</span>)</a></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-9-1.png" width="672"></p>
-<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb14-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.L2.FOMC, <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.48.1 
+<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb17-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.L2.FOMC, <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.49.6 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Fri Jul  5 15:52:55 2019 
-## Date of summary: Fri Jul  5 15:52:55 2019 
+## Date of fit:     Tue Jul  9 09:00:23 2019 
+## Date of summary: Tue Jul  9 09:00:23 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 81 model solutions performed in 0.178 s
+## Fitted using 239 model solutions performed in 0.495 s
+## 
+## Error model: Constant variance 
 ## 
-## Weighting: none
+## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 93.95  state
-## alpha     1.00 deparm
-## beta     10.00 deparm
+##              value   type
+## parent_0 93.950000  state
+## alpha     1.000000 deparm
+## beta     10.000000 deparm
+## sigma     2.275722  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##               value lower upper
 ## parent_0  93.950000  -Inf   Inf
 ## log_alpha  0.000000  -Inf   Inf
 ## log_beta   2.302585  -Inf   Inf
+## sigma      2.275722     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error   Lower   Upper
-## parent_0   93.7700     1.8560 89.5700 97.9700
-## log_alpha   0.3180     0.1867 -0.1044  0.7405
-## log_beta    0.2102     0.2943 -0.4555  0.8759
+##           Estimate Std. Error    Lower   Upper
+## parent_0   93.7700     1.6130 90.05000 97.4900
+## log_alpha   0.3180     0.1559 -0.04149  0.6776
+## log_beta    0.2102     0.2493 -0.36460  0.7850
+## sigma       2.2760     0.4645  1.20500  3.3470
 ## 
 ## Parameter correlation:
-##           parent_0 log_alpha log_beta
-## parent_0   1.00000  -0.09553  -0.1863
-## log_alpha -0.09553   1.00000   0.9757
-## log_beta  -0.18628   0.97567   1.0000
-## 
-## Residual standard error: 2.628 on 9 degrees of freedom
+##             parent_0  log_alpha   log_beta      sigma
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-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 -1.387e-07
+## sigma     -7.637e-09 -1.617e-07 -1.387e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
 ##          Estimate t value    Pr(&gt;t)   Lower  Upper
-## parent_0   93.770  50.510 1.173e-12 89.5700 97.970
-## alpha       1.374   5.355 2.296e-04  0.9009  2.097
-## beta        1.234   3.398 3.949e-03  0.6341  2.401
+## parent_0   93.770  58.120 4.267e-12 90.0500 97.490
+## alpha       1.374   6.414 1.030e-04  0.9594  1.969
+## beta        1.234   4.012 1.942e-03  0.6945  2.192
+## sigma       2.276   4.899 5.977e-04  1.2050  3.347
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   6.205       3  3
 ## parent     6.205       3  3
@@ -371,17 +390,15 @@
 <h2 class="hasAnchor">
 <a href="#dfop-fit-for-l2" class="anchor"></a>DFOP fit for L2</h2>
 <p>Fitting the four parameter DFOP model further reduces the <span class="math inline">\(\chi^2\)</span> error level.</p>
-<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb16-1" title="1">m.L2.DFOP &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"DFOP"</span>, FOCUS_<span class="dv">2006</span>_L2_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb16-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L2.DFOP, <span class="dt">show_residuals =</span> <span class="ot">TRUE</span>, <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>,</a>
-<a class="sourceLine" id="cb16-3" title="3">     <span class="dt">main =</span> <span class="st">"FOCUS L2 - DFOP"</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb19-1" title="1">m.L2.DFOP &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"DFOP"</span>, FOCUS_<span class="dv">2006</span>_L2_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
+<a class="sourceLine" id="cb19-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L2.DFOP, <span class="dt">show_residuals =</span> <span class="ot">TRUE</span>, <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>,</a>
+<a class="sourceLine" id="cb19-3" title="3">     <span class="dt">main =</span> <span class="st">"FOCUS L2 - DFOP"</span>)</a></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-10-1.png" width="672"></p>
-<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb17-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.L2.DFOP, <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(m.L2.DFOP, data = FALSE): Could not estimate
-## covariance matrix; singular system.</code></pre>
-<pre><code>## mkin version used for fitting:    0.9.48.1 
+<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb20-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.L2.DFOP, <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.49.6 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Fri Jul  5 15:52:56 2019 
-## Date of summary: Fri Jul  5 15:52:56 2019 
+## Date of fit:     Tue Jul  9 09:00:24 2019 
+## Date of summary: Tue Jul  9 09:00:25 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
@@ -390,16 +407,19 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 336 model solutions performed in 0.752 s
+## Fitted using 572 model solutions performed in 1.193 s
 ## 
-## Weighting: none
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 93.95  state
-## k1        0.10 deparm
-## k2        0.01 deparm
-## g         0.50 deparm
+##              value   type
+## parent_0 93.950000  state
+## k1        0.100000 deparm
+## k2        0.010000 deparm
+## g         0.500000 deparm
+## sigma     1.413899  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##              value lower upper
@@ -407,32 +427,39 @@
 ## log_k1   -2.302585  -Inf   Inf
 ## log_k2   -4.605170  -Inf   Inf
 ## g_ilr     0.000000  -Inf   Inf
+## sigma     1.413899     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##          Estimate Std. Error Lower Upper
-## parent_0  93.9500         NA    NA    NA
-## log_k1     3.1370         NA    NA    NA
-## log_k2    -1.0880         NA    NA    NA
-## g_ilr     -0.2821         NA    NA    NA
+##          Estimate Std. Error      Lower     Upper
+## parent_0  93.9500  9.998e-01    91.5900   96.3100
+## log_k1     3.1370  2.376e+03 -5616.0000 5622.0000
+## log_k2    -1.0880  6.285e-02    -1.2370   -0.9394
+## g_ilr     -0.2821  7.033e-02    -0.4484   -0.1158
+## sigma      1.4140  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
-## Could not estimate covariance matrix; singular system.
-## Residual standard error: 1.732 on 8 degrees of freedom
+##            parent_0     log_k1     log_k2      g_ilr      sigma
+## parent_0  1.000e+00  5.155e-07  2.371e-09  2.665e-01 -6.849e-09
+## log_k1    5.155e-07  1.000e+00  8.434e-05 -1.659e-04 -7.791e-06
+## log_k2    2.371e-09  8.434e-05  1.000e+00 -7.903e-01 -1.262e-08
+## g_ilr     2.665e-01 -1.659e-04 -7.903e-01  1.000e+00  3.241e-08
+## sigma    -6.849e-09 -7.791e-06 -1.262e-08  3.241e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##          Estimate t value Pr(&gt;t) Lower Upper
-## parent_0  93.9500      NA     NA    NA    NA
-## k1        23.0400      NA     NA    NA    NA
-## k2         0.3369      NA     NA    NA    NA
-## g          0.4016      NA     NA    NA    NA
-## 
-## Chi2 error levels in percent:
+##          Estimate   t value    Pr(&gt;t)   Lower   Upper
+## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
+## k1        23.0400 4.303e-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
+## 
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data    2.53       4  2
 ## parent      2.53       4  2
@@ -447,18 +474,18 @@
 <h1 class="hasAnchor">
 <a href="#laboratory-data-l3" class="anchor"></a>Laboratory Data L3</h1>
 <p>The following code defines example dataset L3 from the FOCUS kinetics report, p. 290.</p>
-<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb20-1" title="1">FOCUS_<span class="dv">2006</span>_L3 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a>
-<a class="sourceLine" id="cb20-2" title="2">  <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">30</span>, <span class="dv">60</span>, <span class="dv">91</span>, <span class="dv">120</span>),</a>
-<a class="sourceLine" id="cb20-3" title="3">  <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">97.8</span>, <span class="dv">60</span>, <span class="dv">51</span>, <span class="dv">43</span>, <span class="dv">35</span>, <span class="dv">22</span>, <span class="dv">15</span>, <span class="dv">12</span>))</a>
-<a class="sourceLine" id="cb20-4" title="4">FOCUS_<span class="dv">2006</span>_L3_mkin &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L3)</a></code></pre></div>
+<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb22-1" title="1">FOCUS_<span class="dv">2006</span>_L3 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a>
+<a class="sourceLine" id="cb22-2" title="2">  <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">30</span>, <span class="dv">60</span>, <span class="dv">91</span>, <span class="dv">120</span>),</a>
+<a class="sourceLine" id="cb22-3" title="3">  <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">97.8</span>, <span class="dv">60</span>, <span class="dv">51</span>, <span class="dv">43</span>, <span class="dv">35</span>, <span class="dv">22</span>, <span class="dv">15</span>, <span class="dv">12</span>))</a>
+<a class="sourceLine" id="cb22-4" title="4">FOCUS_<span class="dv">2006</span>_L3_mkin &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L3)</a></code></pre></div>
 <div id="fit-multiple-models" class="section level2">
 <h2 class="hasAnchor">
 <a href="#fit-multiple-models" class="anchor"></a>Fit multiple models</h2>
 <p>As of mkin version 0.9-39 (June 2015), we can fit several models to one or more datasets in one call to the function <code>mmkin</code>. The datasets have to be passed in a list, in this case a named list holding only the L3 dataset prepared above.</p>
-<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb21-1" title="1"><span class="co"># Only use one core here, not to offend the CRAN checks</span></a>
-<a class="sourceLine" id="cb21-2" title="2">mm.L3 &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>), <span class="dt">cores =</span> <span class="dv">1</span>,</a>
-<a class="sourceLine" id="cb21-3" title="3">               <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(<span class="st">"FOCUS L3"</span> =<span class="st"> </span>FOCUS_<span class="dv">2006</span>_L3_mkin), <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb21-4" title="4"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L3)</a></code></pre></div>
+<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb23-1" title="1"><span class="co"># Only use one core here, not to offend the CRAN checks</span></a>
+<a class="sourceLine" id="cb23-2" title="2">mm.L3 &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>), <span class="dt">cores =</span> <span class="dv">1</span>,</a>
+<a class="sourceLine" id="cb23-3" title="3">               <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(<span class="st">"FOCUS L3"</span> =<span class="st"> </span>FOCUS_<span class="dv">2006</span>_L3_mkin), <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
+<a class="sourceLine" id="cb23-4" title="4"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L3)</a></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-12-1.png" width="700"></p>
 <p>The <span class="math inline">\(\chi^2\)</span> error level of 21% as well as the plot suggest that the SFO model does not fit very well. The FOMC model performs better, with an error level at which the <span class="math inline">\(\chi^2\)</span> test passes of 7%. Fitting the four parameter DFOP model further reduces the <span class="math inline">\(\chi^2\)</span> error level considerably.</p>
 </div>
@@ -467,11 +494,11 @@
 <a href="#accessing-mmkin-objects" class="anchor"></a>Accessing mmkin objects</h2>
 <p>The objects returned by mmkin are arranged like a matrix, with models as a row index and datasets as a column index.</p>
 <p>We can extract the summary and plot for <em>e.g.</em> the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.</p>
-<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb22-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(mm.L3[[<span class="st">"DFOP"</span>, <span class="dv">1</span>]])</a></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.48.1 
+<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb24-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(mm.L3[[<span class="st">"DFOP"</span>, <span class="dv">1</span>]])</a></code></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.49.6 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Fri Jul  5 15:52:56 2019 
-## Date of summary: Fri Jul  5 15:52:57 2019 
+## Date of fit:     Tue Jul  9 09:00:26 2019 
+## Date of summary: Tue Jul  9 09:00:27 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
@@ -480,16 +507,19 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 137 model solutions performed in 0.305 s
+## Fitted using 373 model solutions performed in 0.797 s
 ## 
-## Weighting: none
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 97.80  state
-## k1        0.10 deparm
-## k2        0.01 deparm
-## g         0.50 deparm
+##              value   type
+## parent_0 97.800000  state
+## k1        0.100000 deparm
+## k2        0.010000 deparm
+## g         0.500000 deparm
+## sigma     1.017292  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##              value lower upper
@@ -497,37 +527,39 @@
 ## log_k1   -2.302585  -Inf   Inf
 ## log_k2   -4.605170  -Inf   Inf
 ## g_ilr     0.000000  -Inf   Inf
+## sigma     1.017292     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##          Estimate Std. Error   Lower     Upper
-## parent_0  97.7500    1.43800 93.7500 101.70000
-## log_k1    -0.6612    0.13340 -1.0310  -0.29100
-## log_k2    -4.2860    0.05902 -4.4500  -4.12200
-## g_ilr     -0.1229    0.05121 -0.2651   0.01925
+##          Estimate Std. Error   Lower      Upper
+## parent_0  97.7500    1.01900 94.5000 101.000000
+## log_k1    -0.6612    0.10050 -0.9812  -0.341300
+## log_k2    -4.2860    0.04322 -4.4230  -4.148000
+## g_ilr     -0.1229    0.03727 -0.2415  -0.004343
+## sigma      1.0170    0.25430  0.2079   1.827000
 ## 
 ## Parameter correlation:
-##          parent_0  log_k1   log_k2   g_ilr
-## parent_0  1.00000  0.1640  0.01315  0.4253
-## log_k1    0.16400  1.0000  0.46478 -0.5526
-## log_k2    0.01315  0.4648  1.00000 -0.6631
-## g_ilr     0.42526 -0.5526 -0.66310  1.0000
-## 
-## Residual standard error: 1.439 on 4 degrees of freedom
+##            parent_0     log_k1     log_k2      g_ilr      sigma
+## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -6.872e-07
+## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  3.200e-07
+## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  7.673e-07
+## g_ilr     4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -8.731e-07
+## sigma    -6.872e-07  3.200e-07  7.673e-07 -8.731e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
 ##          Estimate t value    Pr(&gt;t)    Lower     Upper
-## parent_0 97.75000  67.970 1.404e-07 93.75000 101.70000
-## k1        0.51620   7.499 8.460e-04  0.35650   0.74750
-## k2        0.01376  16.940 3.557e-05  0.01168   0.01621
-## g         0.45660  25.410 7.121e-06  0.40730   0.50680
+## parent_0 97.75000  95.960 1.248e-06 94.50000 101.00000
+## k1        0.51620   9.947 1.081e-03  0.37490   0.71090
+## k2        0.01376  23.140 8.840e-05  0.01199   0.01579
+## g         0.45660  34.920 2.581e-05  0.41540   0.49850
+## sigma     1.01700   4.000 1.400e-02  0.20790   1.82700
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   2.225       4  4
 ## parent     2.225       4  4
@@ -546,7 +578,7 @@
 ##    60   parent     22.0     23.26 -1.25919
 ##    91   parent     15.0     15.18 -0.18181
 ##   120   parent     12.0     10.19  1.81395</code></pre>
-<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb24-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L3[[<span class="st">"DFOP"</span>, <span class="dv">1</span>]], <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb26-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L3[[<span class="st">"DFOP"</span>, <span class="dv">1</span>]], <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-13-1.png" width="700"></p>
 <p>Here, a look to the model plot, the confidence intervals of the parameters and the correlation matrix suggest that the parameter estimates are reliable, and the DFOP model can be used as the best-fit model based on the <span class="math inline">\(\chi^2\)</span> error level criterion for laboratory data L3.</p>
 <p>This is also an example where the standard t-test for the parameter <code>g_ilr</code> is misleading, as it tests for a significant difference from zero. In this case, zero appears to be the correct value for this parameter, and the confidence interval for the backtransformed parameter <code>g</code> is quite narrow.</p>
@@ -556,67 +588,72 @@
 <h1 class="hasAnchor">
 <a href="#laboratory-data-l4" class="anchor"></a>Laboratory Data L4</h1>
 <p>The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:</p>
-<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb25-1" title="1">FOCUS_<span class="dv">2006</span>_L4 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a>
-<a class="sourceLine" id="cb25-2" title="2">  <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">30</span>, <span class="dv">60</span>, <span class="dv">91</span>, <span class="dv">120</span>),</a>
-<a class="sourceLine" id="cb25-3" title="3">  <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">96.6</span>, <span class="fl">96.3</span>, <span class="fl">94.3</span>, <span class="fl">88.8</span>, <span class="fl">74.9</span>, <span class="fl">59.9</span>, <span class="fl">53.5</span>, <span class="fl">49.0</span>))</a>
-<a class="sourceLine" id="cb25-4" title="4">FOCUS_<span class="dv">2006</span>_L4_mkin &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L4)</a></code></pre></div>
+<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb27-1" title="1">FOCUS_<span class="dv">2006</span>_L4 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a>
+<a class="sourceLine" id="cb27-2" title="2">  <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">30</span>, <span class="dv">60</span>, <span class="dv">91</span>, <span class="dv">120</span>),</a>
+<a class="sourceLine" id="cb27-3" title="3">  <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">96.6</span>, <span class="fl">96.3</span>, <span class="fl">94.3</span>, <span class="fl">88.8</span>, <span class="fl">74.9</span>, <span class="fl">59.9</span>, <span class="fl">53.5</span>, <span class="fl">49.0</span>))</a>
+<a class="sourceLine" id="cb27-4" title="4">FOCUS_<span class="dv">2006</span>_L4_mkin &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L4)</a></code></pre></div>
 <p>Fits of the SFO and FOMC models, plots and summaries are produced below:</p>
-<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb26-1" title="1"><span class="co"># Only use one core here, not to offend the CRAN checks</span></a>
-<a class="sourceLine" id="cb26-2" title="2">mm.L4 &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>), <span class="dt">cores =</span> <span class="dv">1</span>,</a>
-<a class="sourceLine" id="cb26-3" title="3">               <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(<span class="st">"FOCUS L4"</span> =<span class="st"> </span>FOCUS_<span class="dv">2006</span>_L4_mkin),</a>
-<a class="sourceLine" id="cb26-4" title="4">               <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb26-5" title="5"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L4)</a></code></pre></div>
+<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb28-1" title="1"><span class="co"># Only use one core here, not to offend the CRAN checks</span></a>
+<a class="sourceLine" id="cb28-2" title="2">mm.L4 &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>), <span class="dt">cores =</span> <span class="dv">1</span>,</a>
+<a class="sourceLine" id="cb28-3" title="3">               <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(<span class="st">"FOCUS L4"</span> =<span class="st"> </span>FOCUS_<span class="dv">2006</span>_L4_mkin),</a>
+<a class="sourceLine" id="cb28-4" title="4">               <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
+<a class="sourceLine" id="cb28-5" title="5"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L4)</a></code></pre></div>
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-15-1.png" width="700"></p>
 <p>The <span class="math inline">\(\chi^2\)</span> error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is slightly lower for the FOMC model. However, the difference appears negligible.</p>
-<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb27-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(mm.L4[[<span class="st">"SFO"</span>, <span class="dv">1</span>]], <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.48.1 
+<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb29-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(mm.L4[[<span class="st">"SFO"</span>, <span class="dv">1</span>]], <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.49.6 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Fri Jul  5 15:52:57 2019 
-## Date of summary: Fri Jul  5 15:52:57 2019 
+## Date of fit:     Tue Jul  9 09:00:27 2019 
+## Date of summary: Tue Jul  9 09:00:28 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 46 model solutions performed in 0.1 s
+## Fitted using 142 model solutions performed in 0.299 s
 ## 
-## Weighting: none
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##               value   type
-## parent_0       96.6  state
-## k_parent_sink   0.1 deparm
+##                  value   type
+## parent_0      96.60000  state
+## k_parent_sink  0.10000 deparm
+## sigma          3.16181  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##                       value lower upper
 ## parent_0          96.600000  -Inf   Inf
 ## log_k_parent_sink -2.302585  -Inf   Inf
+## sigma              3.161810     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##                   Estimate Std. Error  Lower   Upper
-## parent_0             96.44    1.94900 91.670 101.200
-## log_k_parent_sink    -5.03    0.07999 -5.225  -4.834
+## parent_0            96.440    1.69900 92.070 100.800
+## log_k_parent_sink   -5.030    0.07059 -5.211  -4.848
+## sigma                3.162    0.79050  1.130   5.194
 ## 
 ## Parameter correlation:
-##                   parent_0 log_k_parent_sink
-## parent_0            1.0000            0.5865
-## log_k_parent_sink   0.5865            1.0000
-## 
-## Residual standard error: 3.651 on 6 degrees of freedom
+##                    parent_0 log_k_parent_sink     sigma
+## parent_0          1.000e+00         5.938e-01 3.440e-07
+## log_k_parent_sink 5.938e-01         1.000e+00 5.885e-07
+## sigma             3.440e-07         5.885e-07 1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
 ##                Estimate t value    Pr(&gt;t)     Lower     Upper
-## parent_0      96.440000   49.49 2.283e-09 91.670000 1.012e+02
-## k_parent_sink  0.006541   12.50 8.008e-06  0.005378 7.955e-03
+## parent_0      96.440000   56.77 1.604e-08 92.070000 1.008e+02
+## k_parent_sink  0.006541   14.17 1.578e-05  0.005455 7.842e-03
+## sigma          3.162000    4.00 5.162e-03  1.130000 5.194e+00
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   3.287       2  6
 ## parent     3.287       2  6
@@ -628,60 +665,65 @@
 ## Estimated disappearance times:
 ##        DT50 DT90
 ## parent  106  352</code></pre>
-<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb29-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(mm.L4[[<span class="st">"FOMC"</span>, <span class="dv">1</span>]], <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
-<pre><code>## mkin version used for fitting:    0.9.48.1 
+<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb31-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(mm.L4[[<span class="st">"FOMC"</span>, <span class="dv">1</span>]], <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
+<pre><code>## mkin version used for fitting:    0.9.49.6 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Fri Jul  5 15:52:57 2019 
-## Date of summary: Fri Jul  5 15:52:57 2019 
+## Date of fit:     Tue Jul  9 09:00:28 2019 
+## Date of summary: Tue Jul  9 09:00:28 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 66 model solutions performed in 0.145 s
+## Fitted using 224 model solutions performed in 0.478 s
 ## 
-## Weighting: none
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##          value   type
-## parent_0  96.6  state
-## alpha      1.0 deparm
-## beta      10.0 deparm
+##              value   type
+## parent_0 96.600000  state
+## alpha     1.000000 deparm
+## beta     10.000000 deparm
+## sigma     1.830055  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##               value lower upper
 ## parent_0  96.600000  -Inf   Inf
 ## log_alpha  0.000000  -Inf   Inf
 ## log_beta   2.302585  -Inf   Inf
+## sigma      1.830055     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error  Lower    Upper
-## parent_0   99.1400     1.6800 94.820 103.5000
-## log_alpha  -0.3506     0.3725 -1.308   0.6068
-## log_beta    4.1740     0.5635  2.726   5.6230
+##           Estimate Std. Error   Lower    Upper
+## parent_0   99.1400     1.2670 95.6300 102.7000
+## log_alpha  -0.3506     0.2616 -1.0770   0.3756
+## log_beta    4.1740     0.3938  3.0810   5.2670
+## sigma       1.8300     0.4575  0.5598   3.1000
 ## 
 ## Parameter correlation:
-##           parent_0 log_alpha log_beta
-## parent_0    1.0000   -0.5365  -0.6083
-## log_alpha  -0.5365    1.0000   0.9913
-## log_beta   -0.6083    0.9913   1.0000
-## 
-## Residual standard error: 2.315 on 5 degrees of freedom
+##             parent_0  log_alpha   log_beta      sigma
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08
+## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
 ##          Estimate t value    Pr(&gt;t)   Lower   Upper
-## parent_0  99.1400  59.020 1.322e-08 94.8200 103.500
-## alpha      0.7042   2.685 2.178e-02  0.2703   1.835
-## beta      64.9800   1.775 6.807e-02 15.2600 276.600
+## parent_0  99.1400  78.250 7.993e-08 95.6300 102.700
+## alpha      0.7042   3.823 9.365e-03  0.3407   1.456
+## beta      64.9800   2.540 3.201e-02 21.7800 193.900
+## sigma      1.8300   4.000 8.065e-03  0.5598   3.100
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   2.029       3  5
 ## parent     2.029       3  5
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png
index 7e231d84..f23a4c97 100644
--- a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png
+++ b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png
diff --git a/docs/articles/mkin.html b/docs/articles/mkin.html
index b2df33b7..926bd907 100644
--- a/docs/articles/mkin.html
+++ b/docs/articles/mkin.html
@@ -88,7 +88,7 @@
       <h1>Introduction to mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2019-07-05</h4>
+            <h4 class="date">2019-07-09</h4>
       
       
       <div class="hidden name"><code>mkin.Rmd</code></div>
diff --git a/docs/articles/twa.html b/docs/articles/twa.html
index fabae1bc..30d54f9e 100644
--- a/docs/articles/twa.html
+++ b/docs/articles/twa.html
@@ -88,7 +88,7 @@
       <h1>Calculation of time weighted average concentrations with mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2019-07-05</h4>
+            <h4 class="date">2019-07-09</h4>
       
       
       <div class="hidden name"><code>twa.Rmd</code></div>
diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html
index 2a59b69d..8f3fe97e 100644
--- a/docs/articles/web_only/FOCUS_Z.html
+++ b/docs/articles/web_only/FOCUS_Z.html
@@ -88,7 +88,7 @@
       <h1>Example evaluation of FOCUS dataset Z</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2019-07-05</h4>
+            <h4 class="date">2019-07-09</h4>
       
       
       <div class="hidden name"><code>FOCUS_Z.Rmd</code></div>
@@ -125,82 +125,92 @@
 <div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" title="1">Z<span class="fl">.2</span>a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>),</a>
 <a class="sourceLine" id="cb2-2" title="2">                <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</a></code></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" title="1">m.Z<span class="fl">.2</span>a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z<span class="fl">.2</span>a, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb4-2" title="2"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z<span class="fl">.2</span>a)</a></code></pre></div>
+<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" title="1">m.Z<span class="fl">.2</span>a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z<span class="fl">.2</span>a, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<pre><code>## Warning in mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE): Observations
+## with value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" title="1"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z<span class="fl">.2</span>a)</a></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png" width="700"></p>
-<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.Z<span class="fl">.2</span>a, <span class="dt">data =</span> <span class="ot">FALSE</span>)<span class="op">$</span>bpar</a></code></pre></div>
-<pre><code>##             Estimate se_notrans    t value     Pr(&gt;t)   Lower     Upper
-## Z0_0      9.7015e+01   3.553140 2.7304e+01 1.6792e-21 91.4112 102.61853
-## k_Z0_sink 7.2008e-10   0.226895 3.1736e-09 5.0000e-01  0.0000       Inf
-## k_Z0_Z1   2.2360e+00   0.165074 1.3545e+01 7.3943e-14  1.8393   2.71827
-## k_Z1_sink 4.8212e-01   0.065854 7.3212e+00 3.5520e-08  0.4006   0.58023</code></pre>
+<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.Z<span class="fl">.2</span>a, <span class="dt">data =</span> <span class="ot">FALSE</span>)<span class="op">$</span>bpar</a></code></pre></div>
+<pre><code>##             Estimate se_notrans    t value     Pr(&gt;t)    Lower    Upper
+## Z0_0      9.7015e+01   3.393176 2.8591e+01 6.4352e-21 91.66556 102.3642
+## k_Z0_sink 7.2231e-10   0.225254 3.2067e-09 5.0000e-01  0.00000      Inf
+## k_Z0_Z1   2.2360e+00   0.159134 1.4051e+01 1.1369e-13  1.95303   2.5600
+## k_Z1_sink 4.8212e-01   0.065454 7.3658e+00 5.1186e-08  0.40341   0.5762
+## sigma     4.8041e+00   0.637618 7.5345e+00 3.4431e-08  3.52677   6.0815</code></pre>
 <p>As obvious from the parameter summary (the  component of the summary), the kinetic rate constant from parent compound Z to sink is very small and the t-test for this parameter suggests that it is not significantly different from zero. This suggests, in agreement with the analysis in the FOCUS kinetics report, to simplify the model by removing the pathway to sink.</p>
 <p>A similar result can be obtained when formation fractions are used in the model formulation:</p>
-<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" title="1">Z<span class="fl">.2</span>a.ff &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>),</a>
-<a class="sourceLine" id="cb7-2" title="2">                   <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),</a>
-<a class="sourceLine" id="cb7-3" title="3">                   <span class="dt">use_of_ff =</span> <span class="st">"max"</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" title="1">Z<span class="fl">.2</span>a.ff &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>),</a>
+<a class="sourceLine" id="cb9-2" title="2">                   <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),</a>
+<a class="sourceLine" id="cb9-3" title="3">                   <span class="dt">use_of_ff =</span> <span class="st">"max"</span>)</a></code></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" title="1">m.Z<span class="fl">.2</span>a.ff &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z<span class="fl">.2</span>a.ff, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb9-2" title="2"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z<span class="fl">.2</span>a.ff)</a></code></pre></div>
+<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb11-1" title="1">m.Z<span class="fl">.2</span>a.ff &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z<span class="fl">.2</span>a.ff, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<pre><code>## Warning in mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE): Observations
+## with value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z<span class="fl">.2</span>a.ff)</a></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png" width="700"></p>
-<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.Z<span class="fl">.2</span>a.ff, <span class="dt">data =</span> <span class="ot">FALSE</span>)<span class="op">$</span>bpar</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(m.Z.2a.ff, data = FALSE): Could not estimate
-## covariance matrix; singular system.</code></pre>
-<pre><code>##            Estimate se_notrans t value     Pr(&gt;t) Lower Upper
-## Z0_0       97.01488   3.553145 27.3040 1.6793e-21    NA    NA
-## k_Z0        2.23601   0.216848 10.3114 3.6620e-11    NA    NA
-## k_Z1        0.48212   0.065854  7.3211 3.5520e-08    NA    NA
-## f_Z0_to_Z1  1.00000   0.101473  9.8548 9.7068e-11    NA    NA</code></pre>
+<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb14-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.Z<span class="fl">.2</span>a.ff, <span class="dt">data =</span> <span class="ot">FALSE</span>)<span class="op">$</span>bpar</a></code></pre></div>
+<pre><code>##            Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper
+## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
+## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
+## k_Z1        0.48212   0.063265  7.6207 2.8155e-08  0.40341   0.5762
+## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000
+## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815</code></pre>
 <p>Here, the ilr transformed formation fraction fitted in the model takes a very large value, and the backtransformed formation fraction from parent Z to Z1 is practically unity. Here, the covariance matrix used for the calculation of confidence intervals is not returned as the model is overparameterised.</p>
 <p>A simplified model is obtained by removing the pathway to the sink. </p>
 <p>In the following, we use the parameterisation with formation fractions in order to be able to compare with the results in the FOCUS guidance, and as it makes it easier to use parameters obtained in a previous fit when adding a further metabolite.</p>
-<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1">Z<span class="fl">.3</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb13-2" title="2">               <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>), <span class="dt">use_of_ff =</span> <span class="st">"max"</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb16-1" title="1">Z<span class="fl">.3</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb16-2" title="2">               <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>), <span class="dt">use_of_ff =</span> <span class="st">"max"</span>)</a></code></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb15-1" title="1">m.Z<span class="fl">.3</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z<span class="fl">.3</span>, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb15-2" title="2"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z<span class="fl">.3</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb18-1" title="1">m.Z<span class="fl">.3</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z<span class="fl">.3</span>, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<pre><code>## Warning in mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb20-1" title="1"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z<span class="fl">.3</span>)</a></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png" width="700"></p>
-<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb16-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.Z<span class="fl">.3</span>, <span class="dt">data =</span> <span class="ot">FALSE</span>)<span class="op">$</span>bpar</a></code></pre></div>
-<pre><code>##      Estimate se_notrans t value     Pr(&gt;t)    Lower   Upper
-## Z0_0 97.01488   2.681770  36.176 2.3636e-25 91.52153 102.508
-## k_Z0  2.23601   0.146862  15.225 2.2469e-15  1.95453   2.558
-## k_Z1  0.48212   0.042687  11.294 3.0685e-12  0.40216   0.578</code></pre>
+<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb21-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.Z<span class="fl">.3</span>, <span class="dt">data =</span> <span class="ot">FALSE</span>)<span class="op">$</span>bpar</a></code></pre></div>
+<pre><code>##       Estimate se_notrans t value     Pr(&gt;t)    Lower    Upper
+## Z0_0  97.01488   2.597342  37.352 2.0106e-24 91.67597 102.3538
+## k_Z0   2.23601   0.146904  15.221 9.1477e-15  1.95354   2.5593
+## k_Z1   0.48212   0.041727  11.554 4.8268e-12  0.40355   0.5760
+## sigma  4.80411   0.620208   7.746 1.6110e-08  3.52925   6.0790</code></pre>
 <p>As there is only one transformation product for Z0 and no pathway to sink, the formation fraction is internally fixed to unity.</p>
 </div>
 <div id="metabolites-z2-and-z3" class="section level1">
 <h1 class="hasAnchor">
 <a href="#metabolites-z2-and-z3" class="anchor"></a>Metabolites Z2 and Z3</h1>
 <p>As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as well in the next step. While this step appears questionable on the basis of the above results, it is followed here for the purpose of comparison. Also, in the FOCUS report, it is assumed that there is additional empirical evidence that Z1 quickly and exclusively hydrolyses to Z2.</p>
-<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb18-1" title="1">Z<span class="fl">.5</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb18-2" title="2">               <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb18-3" title="3">               <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>), <span class="dt">use_of_ff =</span> <span class="st">"max"</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb23-1" title="1">Z<span class="fl">.5</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb23-2" title="2">               <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb23-3" title="3">               <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>), <span class="dt">use_of_ff =</span> <span class="st">"max"</span>)</a></code></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb20-1" title="1">m.Z<span class="fl">.5</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z<span class="fl">.5</span>, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb20-2" title="2"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z<span class="fl">.5</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb25-1" title="1">m.Z<span class="fl">.5</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z<span class="fl">.5</span>, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<pre><code>## Warning in mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
+## value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb27-1" title="1"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z<span class="fl">.5</span>)</a></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png" width="700"></p>
 <p>Finally, metabolite Z3 is added to the model. We use the optimised differential equation parameter values from the previous fit in order to accelerate the optimization.</p>
-<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb21-1" title="1">Z.FOCUS &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb21-2" title="2">                   <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb21-3" title="3">                   <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),</a>
-<a class="sourceLine" id="cb21-4" title="4">                   <span class="dt">Z3 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),</a>
-<a class="sourceLine" id="cb21-5" title="5">                   <span class="dt">use_of_ff =</span> <span class="st">"max"</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb28-1" title="1">Z.FOCUS &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb28-2" title="2">                   <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb28-3" title="3">                   <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),</a>
+<a class="sourceLine" id="cb28-4" title="4">                   <span class="dt">Z3 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),</a>
+<a class="sourceLine" id="cb28-5" title="5">                   <span class="dt">use_of_ff =</span> <span class="st">"max"</span>)</a></code></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb23-1" title="1">m.Z.FOCUS &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.FOCUS, FOCUS_<span class="dv">2006</span>_Z_mkin,</a>
-<a class="sourceLine" id="cb23-2" title="2">                     <span class="dt">parms.ini =</span> m.Z<span class="fl">.5</span><span class="op">$</span>bparms.ode,</a>
-<a class="sourceLine" id="cb23-3" title="3">                     <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
-<pre><code>## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation by method Port did not converge:
-## false convergence (8)</code></pre>
-<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb25-1" title="1"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.FOCUS)</a></code></pre></div>
+<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb30-1" title="1">m.Z.FOCUS &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.FOCUS, FOCUS_<span class="dv">2006</span>_Z_mkin,</a>
+<a class="sourceLine" id="cb30-2" title="2">                     <span class="dt">parms.ini =</span> m.Z<span class="fl">.5</span><span class="op">$</span>bparms.ode,</a>
+<a class="sourceLine" id="cb30-3" title="3">                     <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<pre><code>## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.
+## 5$bparms.ode, : Observations with value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb32"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb32-1" title="1"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.FOCUS)</a></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png" width="700"></p>
-<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb26-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.Z.FOCUS, <span class="dt">data =</span> <span class="ot">FALSE</span>)<span class="op">$</span>bpar</a></code></pre></div>
-<pre><code>##             Estimate se_notrans t value     Pr(&gt;t)     Lower     Upper
-## Z0_0       96.838695   2.058856 47.0352 5.5825e-44 92.705465 100.97192
-## k_Z0        2.215407   0.118130 18.7540 7.7427e-25  1.990629   2.46557
-## k_Z1        0.478300   0.029289 16.3305 3.3382e-22  0.422974   0.54086
-## k_Z2        0.451619   0.044213 10.2146 3.1113e-14  0.371037   0.54970
-## k_Z3        0.058693   0.014295  4.1058 7.2882e-05  0.035996   0.09570
-## f_Z2_to_Z3  0.471507   0.057053  8.2643 2.8118e-11  0.360388   0.58552</code></pre>
-<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb28-1" title="1"><span class="kw"><a href="../../reference/endpoints.html">endpoints</a></span>(m.Z.FOCUS)</a></code></pre></div>
+<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb33-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.Z.FOCUS, <span class="dt">data =</span> <span class="ot">FALSE</span>)<span class="op">$</span>bpar</a></code></pre></div>
+<pre><code>##             Estimate se_notrans t value     Pr(&gt;t)     Lower      Upper
+## Z0_0       96.838607   1.994273 48.5584 4.0283e-42 92.826626 100.850589
+## k_Z0        2.215405   0.118459 18.7018 1.0415e-23  1.989465   2.467003
+## k_Z1        0.478300   0.028257 16.9267 6.2408e-22  0.424701   0.538662
+## k_Z2        0.451618   0.042138 10.7177 1.6308e-14  0.374328   0.544867
+## k_Z3        0.058693   0.015246  3.8498 1.7806e-04  0.034805   0.098978
+## f_Z2_to_Z3  0.471508   0.058352  8.0804 9.6648e-11  0.357735   0.588320
+## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736</code></pre>
+<div class="sourceCode" id="cb35"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb35-1" title="1"><span class="kw"><a href="../../reference/endpoints.html">endpoints</a></span>(m.Z.FOCUS)</a></code></pre></div>
 <pre><code>## $ff
 ##   Z2_Z3 Z2_sink 
 ## 0.47151 0.52849 
@@ -212,8 +222,8 @@
 ##        DT50    DT90
 ## Z0  0.31288  1.0394
 ## Z1  1.44919  4.8141
-## Z2  1.53480  5.0985
-## Z3 11.80969 39.2310</code></pre>
+## Z2  1.53481  5.0985
+## Z3 11.80965 39.2308</code></pre>
 <p>This fit corresponds to the final result chosen in Appendix 7 of the FOCUS report. Confidence intervals returned by mkin are based on internally transformed parameters, however.</p>
 </div>
 <div id="using-the-sforb-model" class="section level1">
@@ -221,77 +231,116 @@
 <a href="#using-the-sforb-model" class="anchor"></a>Using the SFORB model</h1>
 <p>As the FOCUS report states, there is a certain tailing of the time course of metabolite Z3. Also, the time course of the parent compound is not fitted very well using the SFO model, as residues at a certain low level remain.</p>
 <p>Therefore, an additional model is offered here, using the single first-order reversible binding (SFORB) model for metabolite Z3. As expected, the <span class="math inline">\(\chi^2\)</span> error level is lower for metabolite Z3 using this model and the graphical fit for Z3 is improved. However, the covariance matrix is not returned.</p>
-<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb30-1" title="1">Z.mkin<span class="fl">.1</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb30-2" title="2">                    <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb30-3" title="3">                    <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),</a>
-<a class="sourceLine" id="cb30-4" title="4">                    <span class="dt">Z3 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>))</a></code></pre></div>
+<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb37-1" title="1">Z.mkin<span class="fl">.1</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb37-2" title="2">                    <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb37-3" title="3">                    <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),</a>
+<a class="sourceLine" id="cb37-4" title="4">                    <span class="dt">Z3 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>))</a></code></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb32"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb32-1" title="1">m.Z.mkin<span class="fl">.1</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.mkin<span class="fl">.1</span>, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb32-2" title="2"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.mkin<span class="fl">.1</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb39"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb39-1" title="1">m.Z.mkin<span class="fl">.1</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.mkin<span class="fl">.1</span>, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<pre><code>## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations
+## with value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb41"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb41-1" title="1"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.mkin<span class="fl">.1</span>)</a></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png" width="700"></p>
-<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb33-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.Z.mkin<span class="fl">.1</span>, <span class="dt">data =</span> <span class="ot">FALSE</span>)<span class="op">$</span>cov.unscaled</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(m.Z.mkin.1, data = FALSE): Could not estimate
-## covariance matrix; singular system.</code></pre>
-<pre><code>## NULL</code></pre>
+<div class="sourceCode" id="cb42"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb42-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.Z.mkin<span class="fl">.1</span>, <span class="dt">data =</span> <span class="ot">FALSE</span>)<span class="op">$</span>cov.unscaled</a></code></pre></div>
+<pre><code>##                            Z0_0 log_k_Z0_Z1 log_k_Z1_Z2 log_k_Z2_sink
+## Z0_0                 3.8375e+00  5.4918e-03  3.0584e-02    1.2969e-01
+## log_k_Z0_Z1          5.4918e-03  2.7613e-03 -1.8820e-04    2.6634e-04
+## log_k_Z1_Z2          3.0584e-02 -1.8820e-04  3.3807e-03    3.2177e-03
+## log_k_Z2_sink        1.2969e-01  2.6634e-04  3.2177e-03    3.4256e-02
+## log_k_Z2_Z3_free    -2.4223e-02 -2.6169e-04 -1.1845e-03   -8.1134e-03
+## log_k_Z3_free_sink  -6.5467e-02 -4.0815e-04 -3.2978e-03   -3.6010e-02
+## log_k_Z3_free_bound -6.0659e-02 -4.4768e-04 -3.0588e-03   -3.9074e-02
+## log_k_Z3_bound_free  5.2844e-01  4.5458e-03  7.9800e-03    4.6274e-02
+## sigma                2.0366e-10 -3.4658e-10  8.9910e-11   -2.5946e-10
+##                     log_k_Z2_Z3_free log_k_Z3_free_sink
+## Z0_0                     -2.4223e-02        -6.5467e-02
+## log_k_Z0_Z1              -2.6169e-04        -4.0815e-04
+## log_k_Z1_Z2              -1.1845e-03        -3.2978e-03
+## log_k_Z2_sink            -8.1134e-03        -3.6010e-02
+## log_k_Z2_Z3_free          1.5500e-02         2.1583e-02
+## log_k_Z3_free_sink        2.1583e-02         7.5705e-02
+## log_k_Z3_free_bound       2.5836e-02         1.1964e-01
+## log_k_Z3_bound_free       5.2534e-02         2.9441e-01
+## sigma                     1.3063e-10         3.4170e-10
+##                     log_k_Z3_free_bound log_k_Z3_bound_free       sigma
+## Z0_0                        -6.0659e-02          5.2844e-01  2.0366e-10
+## log_k_Z0_Z1                 -4.4768e-04          4.5458e-03 -3.4658e-10
+## log_k_Z1_Z2                 -3.0588e-03          7.9800e-03  8.9910e-11
+## log_k_Z2_sink               -3.9074e-02          4.6274e-02 -2.5946e-10
+## log_k_Z2_Z3_free             2.5836e-02          5.2534e-02  1.3063e-10
+## log_k_Z3_free_sink           1.1964e-01          2.9441e-01  3.4170e-10
+## log_k_Z3_free_bound          6.5902e-01          5.4737e+00 -6.7704e-10
+## log_k_Z3_bound_free          5.4737e+00          2.8722e+08  7.2421e-02
+## sigma                       -6.7704e-10          7.2421e-02  1.4170e-01</code></pre>
 <p>Therefore, a further stepwise model building is performed starting from the stage of parent and two metabolites, starting from the assumption that the model fit for the parent compound can be improved by using the SFORB model.</p>
-<div class="sourceCode" id="cb36"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb36-1" title="1">Z.mkin<span class="fl">.3</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb36-2" title="2">                    <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb36-3" title="3">                    <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</a></code></pre></div>
+<div class="sourceCode" id="cb44"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb44-1" title="1">Z.mkin<span class="fl">.3</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb44-2" title="2">                    <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb44-3" title="3">                    <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</a></code></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb38"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb38-1" title="1">m.Z.mkin<span class="fl">.3</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.mkin<span class="fl">.3</span>, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb38-2" title="2"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.mkin<span class="fl">.3</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb46"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb46-1" title="1">m.Z.mkin<span class="fl">.3</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.mkin<span class="fl">.3</span>, FOCUS_<span class="dv">2006</span>_Z_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<pre><code>## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations
+## with value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb48"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb48-1" title="1"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.mkin<span class="fl">.3</span>)</a></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png" width="700"></p>
 <p>This results in a much better representation of the behaviour of the parent compound Z0.</p>
 <p>Finally, Z3 is added as well. These models appear overparameterised (no covariance matrix returned) if the sink for Z1 is left in the models.</p>
-<div class="sourceCode" id="cb39"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb39-1" title="1">Z.mkin<span class="fl">.4</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb39-2" title="2">                    <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb39-3" title="3">                    <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),</a>
-<a class="sourceLine" id="cb39-4" title="4">                    <span class="dt">Z3 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</a></code></pre></div>
+<div class="sourceCode" id="cb49"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb49-1" title="1">Z.mkin<span class="fl">.4</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb49-2" title="2">                    <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb49-3" title="3">                    <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),</a>
+<a class="sourceLine" id="cb49-4" title="4">                    <span class="dt">Z3 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</a></code></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb41"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb41-1" title="1">m.Z.mkin<span class="fl">.4</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.mkin<span class="fl">.4</span>, FOCUS_<span class="dv">2006</span>_Z_mkin,</a>
-<a class="sourceLine" id="cb41-2" title="2">                      <span class="dt">parms.ini =</span> m.Z.mkin<span class="fl">.3</span><span class="op">$</span>bparms.ode,</a>
-<a class="sourceLine" id="cb41-3" title="3">                      <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb41-4" title="4"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.mkin<span class="fl">.4</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb51"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb51-1" title="1">m.Z.mkin<span class="fl">.4</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.mkin<span class="fl">.4</span>, FOCUS_<span class="dv">2006</span>_Z_mkin,</a>
+<a class="sourceLine" id="cb51-2" title="2">                      <span class="dt">parms.ini =</span> m.Z.mkin<span class="fl">.3</span><span class="op">$</span>bparms.ode,</a>
+<a class="sourceLine" id="cb51-3" title="3">                      <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<pre><code>## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
+## 3$bparms.ode, : Observations with value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb53"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb53-1" title="1"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.mkin<span class="fl">.4</span>)</a></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png" width="700"></p>
 <p>The error level of the fit, but especially of metabolite Z3, can be improved if the SFORB model is chosen for this metabolite, as this model is capable of representing the tailing of the metabolite decline phase.</p>
-<div class="sourceCode" id="cb42"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb42-1" title="1">Z.mkin<span class="fl">.5</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb42-2" title="2">                    <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
-<a class="sourceLine" id="cb42-3" title="3">                    <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),</a>
-<a class="sourceLine" id="cb42-4" title="4">                    <span class="dt">Z3 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>))</a></code></pre></div>
+<div class="sourceCode" id="cb54"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb54-1" title="1">Z.mkin<span class="fl">.5</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">Z0 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>, <span class="st">"Z1"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb54-2" title="2">                    <span class="dt">Z1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z2"</span>, <span class="dt">sink =</span> <span class="ot">FALSE</span>),</a>
+<a class="sourceLine" id="cb54-3" title="3">                    <span class="dt">Z2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"Z3"</span>),</a>
+<a class="sourceLine" id="cb54-4" title="4">                    <span class="dt">Z3 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFORB"</span>))</a></code></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb44"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb44-1" title="1">m.Z.mkin<span class="fl">.5</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.mkin<span class="fl">.5</span>, FOCUS_<span class="dv">2006</span>_Z_mkin,</a>
-<a class="sourceLine" id="cb44-2" title="2">                      <span class="dt">parms.ini =</span> m.Z.mkin<span class="fl">.4</span><span class="op">$</span>bparms.ode[<span class="dv">1</span><span class="op">:</span><span class="dv">4</span>],</a>
-<a class="sourceLine" id="cb44-3" title="3">                      <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb44-4" title="4"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.mkin<span class="fl">.5</span>)</a></code></pre></div>
+<div class="sourceCode" id="cb56"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb56-1" title="1">m.Z.mkin<span class="fl">.5</span> &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.mkin<span class="fl">.5</span>, FOCUS_<span class="dv">2006</span>_Z_mkin,</a>
+<a class="sourceLine" id="cb56-2" title="2">                      <span class="dt">parms.ini =</span> m.Z.mkin<span class="fl">.4</span><span class="op">$</span>bparms.ode[<span class="dv">1</span><span class="op">:</span><span class="dv">4</span>],</a>
+<a class="sourceLine" id="cb56-3" title="3">                      <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<pre><code>## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
+## 4$bparms.ode[1:4], : Observations with value of zero were removed from the
+## data</code></pre>
+<div class="sourceCode" id="cb58"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb58-1" title="1"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.mkin<span class="fl">.5</span>)</a></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png" width="700"></p>
 <p>The summary view of the backtransformed parameters shows that we get no confidence intervals due to overparameterisation. As the optimized  is excessively small, it seems reasonable to fix it to zero.</p>
-<div class="sourceCode" id="cb45"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb45-1" title="1">m.Z.mkin<span class="fl">.5</span>a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.mkin<span class="fl">.5</span>, FOCUS_<span class="dv">2006</span>_Z_mkin,</a>
-<a class="sourceLine" id="cb45-2" title="2">                       <span class="dt">parms.ini =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(m.Z.mkin<span class="fl">.5</span><span class="op">$</span>bparms.ode[<span class="dv">1</span><span class="op">:</span><span class="dv">7</span>],</a>
-<a class="sourceLine" id="cb45-3" title="3">                                     <span class="dt">k_Z3_bound_free =</span> <span class="dv">0</span>),</a>
-<a class="sourceLine" id="cb45-4" title="4">                       <span class="dt">fixed_parms =</span> <span class="st">"k_Z3_bound_free"</span>,</a>
-<a class="sourceLine" id="cb45-5" title="5">                       <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb45-6" title="6"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.mkin<span class="fl">.5</span>a)</a></code></pre></div>
+<div class="sourceCode" id="cb59"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb59-1" title="1">m.Z.mkin<span class="fl">.5</span>a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(Z.mkin<span class="fl">.5</span>, FOCUS_<span class="dv">2006</span>_Z_mkin,</a>
+<a class="sourceLine" id="cb59-2" title="2">                       <span class="dt">parms.ini =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(m.Z.mkin<span class="fl">.5</span><span class="op">$</span>bparms.ode[<span class="dv">1</span><span class="op">:</span><span class="dv">7</span>],</a>
+<a class="sourceLine" id="cb59-3" title="3">                                     <span class="dt">k_Z3_bound_free =</span> <span class="dv">0</span>),</a>
+<a class="sourceLine" id="cb59-4" title="4">                       <span class="dt">fixed_parms =</span> <span class="st">"k_Z3_bound_free"</span>,</a>
+<a class="sourceLine" id="cb59-5" title="5">                       <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
+<pre><code>## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = c(m.Z.mkin.
+## 5$bparms.ode[1:7], : Observations with value of zero were removed from the
+## data</code></pre>
+<div class="sourceCode" id="cb61"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb61-1" title="1"><span class="kw"><a href="../../reference/plot.mkinfit.html">plot_sep</a></span>(m.Z.mkin<span class="fl">.5</span>a)</a></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png" width="700"></p>
 <p>As expected, the residual plots for Z0 and Z3 are more random than in the case of the all SFO model for which they were shown above. In conclusion, the model  is proposed as the best-fit model for the dataset from Appendix 7 of the FOCUS report.</p>
 <p>A graphical representation of the confidence intervals can finally be obtained.</p>
-<div class="sourceCode" id="cb46"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb46-1" title="1"><span class="kw"><a href="../../reference/mkinparplot.html">mkinparplot</a></span>(m.Z.mkin<span class="fl">.5</span>a)</a></code></pre></div>
+<div class="sourceCode" id="cb62"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb62-1" title="1"><span class="kw"><a href="../../reference/mkinparplot.html">mkinparplot</a></span>(m.Z.mkin<span class="fl">.5</span>a)</a></code></pre></div>
 <p><img src="FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png" width="700"></p>
 <p>The endpoints obtained with this model are</p>
-<div class="sourceCode" id="cb47"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb47-1" title="1"><span class="kw"><a href="../../reference/endpoints.html">endpoints</a></span>(m.Z.mkin<span class="fl">.5</span>a)</a></code></pre></div>
+<div class="sourceCode" id="cb63"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb63-1" title="1"><span class="kw"><a href="../../reference/endpoints.html">endpoints</a></span>(m.Z.mkin<span class="fl">.5</span>a)</a></code></pre></div>
 <pre><code>## $ff
 ##   Z0_free_Z1        Z1_Z2      Z2_sink   Z2_Z3_free Z3_free_sink 
 ##      1.00000      1.00000      0.46344      0.53656      1.00000 
 ## 
 ## $SFORB
 ##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
-## 2.4471359 0.0075125 0.0800071 0.0000000 
+## 2.4471381 0.0075124 0.0800075 0.0000000 
 ## 
 ## $distimes
 ##      DT50   DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3043 1.1848    0.28325     92.266         NA         NA
+## Z0 0.3043 1.1848    0.28325     92.267         NA         NA
 ## Z1 1.5148 5.0320         NA         NA         NA         NA
 ## Z2 1.6414 5.4526         NA         NA         NA         NA
-## Z3     NA     NA         NA         NA     8.6636        Inf</code></pre>
+## Z3     NA     NA         NA         NA     8.6635        Inf</code></pre>
 <p>It is clear the degradation rate of Z3 towards the end of the experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the system of two differential equations representing the SFORB system for Z3, corresponding to the slower rate constant of the DFOP model) is reported to be infinity. However, this appears to be a feature of the data.</p>
 </div>
 <div id="references" class="section level1">
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png
index 2df6eb44..471db177 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
index 7090c421..3c983f21 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
index 7b98d13d..0e0a78a9 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
index bce36d10..d7dd85a5 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
index 415f29f0..7764f4e2 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png
index 3f49dfa6..d24b8a40 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png
index 41c863dc..dd8c1e0a 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png
index d898f299..45a32027 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
index 3e58f8b6..18832ed2 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png
index f7e57fb3..0d3b4d1a 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
index c61388ab..898e6190 100644
--- a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
+++ b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
diff --git a/docs/articles/web_only/NAFTA_examples.html b/docs/articles/web_only/NAFTA_examples.html
index c614166d..b8a5215d 100644
--- a/docs/articles/web_only/NAFTA_examples.html
+++ b/docs/articles/web_only/NAFTA_examples.html
@@ -88,7 +88,7 @@
       <h1>Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2019-07-05</h4>
+            <h4 class="date">2019-07-09</h4>
       
       
       <div class="hidden name"><code>NAFTA_examples.Rmd</code></div>
@@ -111,13 +111,11 @@
 <h2 class="hasAnchor">
 <a href="#example-on-page-5-upper-panel" class="anchor"></a>Example on page 5, upper panel</h2>
 <div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" title="1">p5a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p5a"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p5a)</a></code></pre></div>
+<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p5a)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p5a-1.png" width="700"></p>
-<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p5a)</a></code></pre></div>
+<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p5a)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 465.21753  56.27506  32.06401 
@@ -128,21 +126,24 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(&gt;t)  Lower   Upper
-## parent_0       95.8401 1.10e-21 92.121 99.5597
-## k_parent_sink   0.0102 1.71e-12  0.009  0.0117
+## parent_0       95.8401 4.67e-21 92.245 99.4357
+## k_parent_sink   0.0102 3.92e-12  0.009  0.0117
+## sigma           4.8230 3.81e-06  3.214  6.4318
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            1.01e+02 2.37e-26 9.89e+01 1.03e+02
-## k__iore_parent_sink 1.54e-05 8.73e-02 3.48e-06 6.85e-05
-## N_parent            2.57e+00 1.14e-11 2.22e+00 2.92e+00
+##                     Estimate Pr(&gt;t)    Lower    Upper
+## parent_0            1.01e+02     NA 9.91e+01 1.02e+02
+## k__iore_parent_sink 1.54e-05     NA 4.08e-06 5.84e-05
+## N_parent            2.57e+00     NA 2.25e+00 2.89e+00
+## sigma               1.68e+00     NA 1.12e+00 2.24e+00
 ## 
 ## $DFOP
-##          Estimate   Pr(&gt;t) Lower Upper
-## parent_0 9.99e+01 4.33e-27    NA    NA
-## k1       2.67e-02 3.17e-05    NA    NA
-## k2       2.86e-12 5.00e-01    NA    NA
-## g        6.47e-01 2.13e-05    NA    NA
+##          Estimate   Pr(&gt;t)   Lower    Upper
+## parent_0 9.99e+01 1.41e-26 98.8116 101.0810
+## k1       2.67e-02 5.05e-06  0.0243   0.0295
+## k2       2.86e-12 5.00e-01  0.0000      Inf
+## g        6.47e-01 3.67e-06  0.6248   0.6677
+## sigma    1.27e+00 8.91e-06  0.8395   1.6929
 ## 
 ## 
 ## DTx values:
@@ -152,19 +153,17 @@
 ## DFOP 55.5 4.42e+11 2.42e+11
 ## 
 ## Representative half-life:
-## [1] 321.5119</code></pre>
+## [1] 321.51</code></pre>
 </div>
 <div id="example-on-page-5-lower-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-5-lower-panel" class="anchor"></a>Example on page 5, lower panel</h2>
-<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" title="1">p5b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p5b"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" title="1">p5b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p5b"</span>]])</a></code></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb12-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p5b)</a></code></pre></div>
+<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p5b)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p5b-1.png" width="700"></p>
-<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p5b)</a></code></pre></div>
+<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb11-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p5b)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 94.81123 10.10936  7.55871 
@@ -175,21 +174,24 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0        96.497 2.62e-25 94.77653 98.21774
-## k_parent_sink    0.008 1.35e-14  0.00736  0.00871
+## parent_0        96.497 2.32e-24 94.85271 98.14155
+## k_parent_sink    0.008 3.42e-14  0.00737  0.00869
+## sigma            2.295 1.22e-05  1.47976  3.11036
 ## 
 ## $IORE
 ##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            9.85e+01 1.02e-29 9.78e+01 9.93e+01
-## k__iore_parent_sink 1.53e-04 1.15e-02 6.60e-05 3.56e-04
-## N_parent            1.94e+00 8.18e-13 1.74e+00 2.14e+00
+## parent_0            9.85e+01 1.17e-28 9.79e+01 9.92e+01
+## k__iore_parent_sink 1.53e-04 6.50e-03 7.21e-05 3.26e-04
+## N_parent            1.94e+00 5.88e-13 1.76e+00 2.12e+00
+## sigma               7.49e-01 1.63e-05 4.82e-01 1.02e+00
 ## 
 ## $DFOP
-##          Estimate   Pr(&gt;t) Lower Upper
-## parent_0 9.84e+01 1.90e-28    NA    NA
-## k1       1.55e-02 2.83e-03    NA    NA
-## k2       1.16e-11 5.00e-01    NA    NA
-## g        6.89e-01 1.31e-02    NA    NA
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0 9.84e+01 1.24e-27 97.8078 98.9187
+## k1       1.55e-02 4.10e-04  0.0143  0.0167
+## k2       1.16e-11 5.00e-01  0.0000     Inf
+## g        6.89e-01 2.92e-03  0.6626  0.7142
+## sigma    6.48e-01 2.38e-05  0.4147  0.8813
 ## 
 ## 
 ## DTx values:
@@ -199,19 +201,17 @@
 ## DFOP 83.6 9.80e+10 5.98e+10
 ## 
 ## Representative half-life:
-## [1] 215.8655</code></pre>
+## [1] 215.87</code></pre>
 </div>
 <div id="example-on-page-6" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-6" class="anchor"></a>Example on page 6</h2>
-<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb15-1" title="1">p6 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p6"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1">p6 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p6"</span>]])</a></code></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb19-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p6)</a></code></pre></div>
+<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb16-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p6)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p6-1.png" width="700"></p>
-<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb20-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p6)</a></code></pre></div>
+<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb17-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p6)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 188.45361  51.00699  42.46931 
@@ -222,21 +222,24 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(&gt;t)   Lower   Upper
-## parent_0       94.7759 1.25e-24 92.2558 97.2960
-## k_parent_sink   0.0179 2.35e-16  0.0166  0.0194
+## parent_0       94.7759 7.29e-24 92.3478 97.2039
+## k_parent_sink   0.0179 8.02e-16  0.0166  0.0194
+## sigma           3.0696 3.81e-06  2.0456  4.0936
 ## 
 ## $IORE
 ##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            97.12446 5.62e-27 95.49343 98.75549
-## k__iore_parent_sink  0.00252 3.54e-03  0.00126  0.00502
-## N_parent             1.49587 6.13e-13  1.32380  1.66794
+## parent_0            97.12446 2.63e-26 95.62461 98.62431
+## k__iore_parent_sink  0.00252 1.95e-03  0.00134  0.00472
+## N_parent             1.49587 4.07e-13  1.33896  1.65279
+## sigma                1.59698 5.05e-06  1.06169  2.13227
 ## 
 ## $DFOP
-##          Estimate   Pr(&gt;t) Lower Upper
-## parent_0 9.66e+01 4.17e-26    NA    NA
-## k1       2.55e-02 2.12e-05    NA    NA
-## k2       4.90e-11 5.00e-01    NA    NA
-## g        8.61e-01 2.10e-05    NA    NA
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0 9.66e+01 1.57e-25 95.3476 97.8979
+## k1       2.55e-02 7.33e-06  0.0233  0.0278
+## k2       4.90e-11 5.00e-01  0.0000     Inf
+## g        8.61e-01 7.55e-06  0.8314  0.8867
+## sigma    1.46e+00 6.93e-06  0.9661  1.9483
 ## 
 ## 
 ## DTx values:
@@ -246,19 +249,17 @@
 ## DFOP 34.1 6.66e+09 1.41e+10
 ## 
 ## Representative half-life:
-## [1] 53.16582</code></pre>
+## [1] 53.17</code></pre>
 </div>
 <div id="example-on-page-7" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-7" class="anchor"></a>Example on page 7</h2>
-<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb22-1" title="1">p7 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p7"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb19-1" title="1">p7 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p7"</span>]])</a></code></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb26-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p7)</a></code></pre></div>
+<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb22-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p7)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p7-1.png" width="700"></p>
-<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb27-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p7)</a></code></pre></div>
+<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb23-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p7)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3661.661 3195.030 3174.145 
@@ -269,21 +270,24 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0      96.41796 1.52e-53 93.29554 99.54038
-## k_parent_sink  0.00735 3.59e-21  0.00641  0.00842
+## parent_0      96.41796 4.80e-53 93.32245 99.51347
+## k_parent_sink  0.00735 7.64e-21  0.00641  0.00843
+## sigma          7.94557 1.83e-15  6.46713  9.42401
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            9.92e+01 7.33e-49 9.53e+01 1.03e+02
-## k__iore_parent_sink 1.60e-05 3.47e-01 9.98e-08 2.57e-03
-## N_parent            2.45e+00 6.14e-05 1.26e+00 3.63e+00
+##                     Estimate Pr(&gt;t)    Lower    Upper
+## parent_0            9.92e+01     NA 9.55e+01 1.03e+02
+## k__iore_parent_sink 1.60e-05     NA 1.45e-07 1.77e-03
+## N_parent            2.45e+00     NA 1.35e+00 3.54e+00
+## sigma               7.42e+00     NA 6.04e+00 8.80e+00
 ## 
 ## $DFOP
-##          Estimate   Pr(&gt;t) Lower Upper
-## parent_0 9.89e+01 8.13e-48    NA    NA
-## k1       1.81e-02 2.20e-01    NA    NA
-## k2       1.97e-10 5.00e-01    NA    NA
-## g        6.06e-01 2.60e-01    NA    NA
+##          Estimate   Pr(&gt;t)   Lower    Upper
+## parent_0 9.89e+01 9.44e-49 95.4640 102.2573
+## k1       1.81e-02 1.75e-01  0.0116   0.0281
+## k2       1.97e-10 5.00e-01  0.0000      Inf
+## g        6.06e-01 2.19e-01  0.4826   0.7178
+## sigma    7.40e+00 2.97e-15  6.0201   8.7754
 ## 
 ## 
 ## DTx values:
@@ -293,7 +297,7 @@
 ## DFOP 96.4 6.97e+09 3.52e+09
 ## 
 ## Representative half-life:
-## [1] 454.5528</code></pre>
+## [1] 454.55</code></pre>
 </div>
 </div>
 <div id="examples-where-the-representative-half-life-deviates-from-the-observed-dt50" class="section level1">
@@ -303,17 +307,12 @@
 <h2 class="hasAnchor">
 <a href="#example-on-page-8" class="anchor"></a>Example on page 8</h2>
 <p>For this dataset, the IORE fit does not converge when the default starting values used by mkin for the IORE model are used. Therefore, a lower value for the rate constant is used here.</p>
-<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb29-1" title="1">p8 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p8"</span>]], <span class="dt">parms.ini =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dt">k__iore_parent_sink =</span> <span class="fl">1e-3</span>))</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.
-
-## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb25-1" title="1">p8 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p8"</span>]], <span class="dt">parms.ini =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dt">k__iore_parent_sink =</span> <span class="fl">1e-3</span>))</a></code></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb33-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p8)</a></code></pre></div>
+<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb28-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p8)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p8-1.png" width="700"></p>
-<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb34-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p8)</a></code></pre></div>
+<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb29-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p8)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 1996.9408  444.9237  547.5616 
@@ -323,24 +322,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##                     Estimate Pr(&gt;t) Lower Upper
-## parent_0            88.16549     NA    NA    NA
-## k__iore_parent_sink  0.00100     NA    NA    NA
-## k_parent_sink        0.00803     NA    NA    NA
+##               Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0      88.16549 6.53e-29 83.37344 92.95754
+## k_parent_sink  0.00803 1.67e-13  0.00674  0.00957
+## sigma          7.44786 4.17e-10  5.66209  9.23363
 ## 
 ## $IORE
 ##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            9.77e+01 1.05e-35 9.44e+01 1.01e+02
-## k__iore_parent_sink 6.14e-05 2.76e-02 2.21e-05 1.71e-04
-## N_parent            2.27e+00 6.00e-19 2.02e+00 2.53e+00
+## parent_0            9.77e+01 7.03e-35 9.44e+01 1.01e+02
+## k__iore_parent_sink 6.14e-05 3.20e-02 2.12e-05 1.78e-04
+## N_parent            2.27e+00 4.23e-18 2.00e+00 2.54e+00
+## sigma               3.52e+00 5.36e-10 2.67e+00 4.36e+00
 ## 
 ## $DFOP
-##                     Estimate Pr(&gt;t) Lower Upper
-## parent_0            95.70619     NA    NA    NA
-## k__iore_parent_sink  0.00100     NA    NA    NA
-## k1                   0.02500     NA    NA    NA
-## k2                   0.00273     NA    NA    NA
-## g                    0.58835     NA    NA    NA
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 95.70619 8.99e-32 91.87941 99.53298
+## k1        0.02500 5.25e-04  0.01422  0.04394
+## k2        0.00273 6.84e-03  0.00125  0.00597
+## g         0.58835 2.84e-06  0.36595  0.77970
+## sigma     3.90001 6.94e-10  2.96260  4.83741
 ## 
 ## 
 ## DTx values:
@@ -350,7 +350,7 @@
 ## DFOP 55.6  517    253.0
 ## 
 ## Representative half-life:
-## [1] 201.0316</code></pre>
+## [1] 201.03</code></pre>
 </div>
 </div>
 <div id="examples-where-sfo-was-not-selected-for-an-abiotic-study" class="section level1">
@@ -359,14 +359,12 @@
 <div id="example-on-page-9-upper-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-9-upper-panel" class="anchor"></a>Example on page 9, upper panel</h2>
-<div class="sourceCode" id="cb36"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb36-1" title="1">p9a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p9a"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb31-1" title="1">p9a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p9a"</span>]])</a></code></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb40"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb40-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p9a)</a></code></pre></div>
+<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb34-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p9a)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p9a-1.png" width="700"></p>
-<div class="sourceCode" id="cb41"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb41-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p9a)</a></code></pre></div>
+<div class="sourceCode" id="cb35"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb35-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p9a)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 839.35238  88.57064   9.93363 
@@ -377,21 +375,24 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(&gt;t)   Lower   Upper
-## parent_0       88.1933 1.12e-12 79.7671 96.6195
-## k_parent_sink   0.0409 9.50e-08  0.0326  0.0513
+## parent_0       88.1933 3.06e-12 79.9447 96.4419
+## k_parent_sink   0.0409 2.07e-07  0.0324  0.0516
+## sigma           7.2429 3.92e-05  4.4768 10.0090
 ## 
 ## $IORE
 ##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            9.89e+01 5.16e-17 9.50e+01 1.03e+02
-## k__iore_parent_sink 1.93e-05 1.48e-01 2.65e-06 1.40e-04
-## N_parent            2.91e+00 3.74e-09 2.43e+00 3.39e+00
+## parent_0            9.89e+01 1.12e-16 9.54e+01 1.02e+02
+## k__iore_parent_sink 1.93e-05 1.13e-01 3.49e-06 1.06e-04
+## N_parent            2.91e+00 1.45e-09 2.50e+00 3.32e+00
+## sigma               2.35e+00 5.31e-05 1.45e+00 3.26e+00
 ## 
 ## $DFOP
-##          Estimate   Pr(&gt;t) Lower Upper
-## parent_0 9.85e+01 1.31e-21    NA    NA
-## k1       1.38e-01 3.63e-09    NA    NA
-## k2       6.02e-13 5.00e-01    NA    NA
-## g        6.52e-01 1.50e-10    NA    NA
+##          Estimate   Pr(&gt;t)  Lower  Upper
+## parent_0 9.85e+01 2.54e-20 97.390 99.672
+## k1       1.38e-01 3.52e-05  0.131  0.146
+## k2       6.02e-13 5.00e-01  0.000    Inf
+## g        6.52e-01 8.13e-06  0.642  0.661
+## sigma    7.88e-01 6.13e-02  0.481  1.095
 ## 
 ## 
 ## DTx values:
@@ -401,20 +402,23 @@
 ## DFOP 10.5 2.07e+12 1.15e+12
 ## 
 ## Representative half-life:
-## [1] 101.4264</code></pre>
+## [1] 101.43</code></pre>
 <p>In this example, the residuals of the SFO indicate a lack of fit of this model, so even if it was an abiotic experiment, the data do not suggest a simple exponential decline.</p>
 </div>
 <div id="example-on-page-9-lower-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-9-lower-panel" class="anchor"></a>Example on page 9, lower panel</h2>
-<div class="sourceCode" id="cb43"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb43-1" title="1">p9b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p9b"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb37-1" title="1">p9b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p9b"</span>]])</a></code></pre></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
+## finite result is doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb47"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb47-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p9b)</a></code></pre></div>
+<div class="sourceCode" id="cb44"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb44-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p9b)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p>
-<div class="sourceCode" id="cb48"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb48-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p9b)</a></code></pre></div>
+<div class="sourceCode" id="cb45"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb45-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p9b)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 35.64867 23.22334 35.64867 
@@ -424,22 +428,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)   Lower  Upper
-## parent_0       94.7123 2.21e-20 93.0673 96.357
-## k_parent_sink   0.0389 1.48e-14  0.0369  0.041
+##               Estimate   Pr(&gt;t)  Lower   Upper
+## parent_0       94.7123 2.15e-19 93.178 96.2464
+## k_parent_sink   0.0389 4.47e-14  0.037  0.0408
+## sigma           1.5957 1.28e-04  0.932  2.2595
 ## 
 ## $IORE
 ##                     Estimate   Pr(&gt;t)   Lower  Upper
-## parent_0              93.863 2.91e-19 92.2996 95.426
-## k__iore_parent_sink    0.127 2.73e-02  0.0457  0.354
-## N_parent               0.711 3.13e-05  0.4605  0.961
+## parent_0              93.863 2.32e-18 92.4565 95.269
+## k__iore_parent_sink    0.127 1.85e-02  0.0504  0.321
+## N_parent               0.711 1.88e-05  0.4843  0.937
+## sigma                  1.288 1.76e-04  0.7456  1.830
 ## 
 ## $DFOP
-##          Estimate Pr(&gt;t) Lower Upper
-## parent_0  94.7123     NA    NA    NA
-## k1         0.0389     NA    NA    NA
-## k2         0.0389     NA    NA    NA
-## g          0.7742     NA    NA    NA
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0  94.7123 1.61e-16 93.1355 96.2891
+## k1         0.0389 1.43e-06  0.0312  0.0485
+## k2         0.0389 6.67e-03  0.0186  0.0812
+## g          0.7742      NaN      NA      NA
+## sigma      1.5957 2.50e-04  0.9135  2.2779
 ## 
 ## 
 ## DTx values:
@@ -449,20 +456,18 @@
 ## DFOP 17.8 59.2     17.8
 ## 
 ## Representative half-life:
-## [1] 14.80012</code></pre>
+## [1] 14.8</code></pre>
 <p>Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days) than PestDF (13.5 days). Presumably, this is related to the fact that PestDF gives a negative value for the proportion of the fast degradation which should be between 0 and 1, inclusive. This parameter is called f in PestDF and g in mkin. In mkin, it is restricted to the interval from 0 to 1.</p>
 </div>
 <div id="example-on-page-10" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-10" class="anchor"></a>Example on page 10</h2>
-<div class="sourceCode" id="cb50"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb50-1" title="1">p10 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p10"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb47"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb47-1" title="1">p10 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p10"</span>]])</a></code></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb54"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb54-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p10)</a></code></pre></div>
+<div class="sourceCode" id="cb50"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb50-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p10)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p>
-<div class="sourceCode" id="cb55"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb55-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p10)</a></code></pre></div>
+<div class="sourceCode" id="cb51"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb51-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p10)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 899.4089 336.4348 899.4089 
@@ -473,21 +478,24 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(&gt;t)   Lower    Upper
-## parent_0      101.7315 4.95e-11 90.9683 112.4947
-## k_parent_sink   0.0495 3.40e-07  0.0393   0.0624
+## parent_0      101.7315 6.42e-11 91.9259 111.5371
+## k_parent_sink   0.0495 1.70e-07  0.0404   0.0607
+## sigma           8.0152 1.28e-04  4.6813  11.3491
 ## 
 ## $IORE
 ##                     Estimate   Pr(&gt;t)  Lower   Upper
-## parent_0               96.86 2.71e-12 89.884 103.826
-## k__iore_parent_sink     2.96 1.31e-01  0.461  19.020
-## N_parent                0.00 5.00e-01 -0.473   0.473
+## parent_0               96.86 3.32e-12 90.848 102.863
+## k__iore_parent_sink     2.96 7.91e-02  0.687  12.761
+## N_parent                0.00 5.00e-01 -0.372   0.372
+## sigma                   4.90 1.77e-04  2.837   6.968
 ## 
 ## $DFOP
-##          Estimate Pr(&gt;t) Lower Upper
-## parent_0 101.7315     NA    NA    NA
-## k1         0.0495     NA    NA    NA
-## k2         0.0495     NA    NA    NA
-## g          0.6634     NA    NA    NA
+##          Estimate   Pr(&gt;t)   Lower    Upper
+## parent_0 101.7315 1.41e-09 91.6534 111.8097
+## k1         0.0495 6.42e-04  0.0301   0.0814
+## k2         0.0495 1.66e-02  0.0200   0.1225
+## g          0.6634 5.00e-01  0.0000   1.0000
+## sigma      8.0152 2.50e-04  4.5886  11.4418
 ## 
 ## 
 ## DTx values:
@@ -497,7 +505,7 @@
 ## DFOP 14.0 46.5    14.00
 ## 
 ## Representative half-life:
-## [1] 8.862193</code></pre>
+## [1] 8.86</code></pre>
 <p>Here, a value below N is given for the IORE model, because the data suggests a faster decline towards the end of the experiment, which appears physically rather unlikely in the case of a photolysis study. It seems PestDF does not constrain N to values above zero, thus the slight difference in IORE model parameters between PestDF and mkin.</p>
 </div>
 </div>
@@ -507,14 +515,12 @@
 <div id="example-on-page-11" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-11" class="anchor"></a>Example on page 11</h2>
-<div class="sourceCode" id="cb57"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb57-1" title="1">p11 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p11"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb53"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb53-1" title="1">p11 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p11"</span>]])</a></code></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb61"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb61-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p11)</a></code></pre></div>
+<div class="sourceCode" id="cb56"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb56-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p11)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p>
-<div class="sourceCode" id="cb62"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb62-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p11)</a></code></pre></div>
+<div class="sourceCode" id="cb57"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb57-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p11)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 579.6805 204.7932 144.7783 
@@ -525,21 +531,24 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0      96.15820 1.56e-13 89.91373 1.02e+02
-## k_parent_sink  0.00321 5.27e-05  0.00218 4.71e-03
+## parent_0      96.15820 4.83e-13 90.24934 1.02e+02
+## k_parent_sink  0.00321 4.71e-05  0.00222 4.64e-03
+## sigma          6.43473 1.28e-04  3.75822 9.11e+00
 ## 
 ## $IORE
 ##                     Estimate Pr(&gt;t)    Lower    Upper
-## parent_0            1.05e+02     NA 9.80e+01 1.11e+02
-## k__iore_parent_sink 3.11e-17     NA 6.88e-25 1.41e-09
-## N_parent            8.36e+00     NA 4.40e+00 1.23e+01
+## parent_0            1.05e+02     NA 9.90e+01 1.10e+02
+## k__iore_parent_sink 3.11e-17     NA 1.35e-20 7.18e-14
+## N_parent            8.36e+00     NA 6.62e+00 1.01e+01
+## sigma               3.82e+00     NA 2.21e+00 5.44e+00
 ## 
 ## $DFOP
-##          Estimate   Pr(&gt;t) Lower Upper
-## parent_0 1.05e+02 7.50e-13    NA    NA
-## k1       4.41e-02 3.34e-02    NA    NA
-## k2       7.25e-13 5.00e-01    NA    NA
-## g        3.22e-01 7.87e-03    NA    NA
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 1.05e+02 9.47e-13  99.9990 109.1224
+## k1       4.41e-02 5.95e-03   0.0296   0.0658
+## k2       7.25e-13 5.00e-01   0.0000      Inf
+## g        3.22e-01 1.45e-03   0.2814   0.3650
+## sigma    3.22e+00 3.52e-04   1.8410   4.5906
 ## 
 ## 
 ## DTx values:
@@ -560,14 +569,14 @@
 <div id="example-on-page-12-upper-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-12-upper-panel" class="anchor"></a>Example on page 12, upper panel</h2>
-<div class="sourceCode" id="cb64"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb64-1" title="1">p12a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p12a"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb59"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb59-1" title="1">p12a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p12a"</span>]])</a></code></pre></div>
+<pre><code>## Warning in summary.mkinfit(x): Could not calculate correlation; no
+## covariance matrix</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb68"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb68-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p12a)</a></code></pre></div>
+<div class="sourceCode" id="cb63"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb63-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p12a)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p>
-<div class="sourceCode" id="cb69"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb69-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p12a)</a></code></pre></div>
+<div class="sourceCode" id="cb64"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb64-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p12a)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 695.4440 220.0685 695.4440 
@@ -578,21 +587,24 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(&gt;t)  Lower   Upper
-## parent_0       100.521 5.61e-12 91.687 109.355
-## k_parent_sink    0.124 7.24e-08  0.102   0.152
+## parent_0       100.521 8.75e-12 92.461 108.581
+## k_parent_sink    0.124 3.61e-08  0.104   0.148
+## sigma            7.048 1.28e-04  4.116   9.980
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)   Lower   Upper
-## parent_0              96.823 1.24e-13 91.5691 102.078
-## k__iore_parent_sink    2.436 3.89e-02  0.7854   7.556
-## N_parent               0.263 3.64e-02 -0.0288   0.554
+##                     Estimate Pr(&gt;t) Lower Upper
+## parent_0              96.823     NA    NA    NA
+## k__iore_parent_sink    2.436     NA    NA    NA
+## N_parent               0.263     NA    NA    NA
+## sigma                  3.965     NA    NA    NA
 ## 
 ## $DFOP
-##          Estimate Pr(&gt;t) Lower Upper
-## parent_0  100.521     NA    NA    NA
-## k1          0.124     NA    NA    NA
-## k2          0.124     NA    NA    NA
-## g           0.877     NA    NA    NA
+##          Estimate   Pr(&gt;t)   Lower   Upper
+## parent_0  100.521 2.74e-10 92.2366 108.805
+## k1          0.124 5.74e-06  0.0958   0.161
+## k2          0.124 6.61e-02  0.0319   0.484
+## g           0.877 5.00e-01  0.0000   1.000
+## sigma       7.048 2.50e-04  4.0349  10.061
 ## 
 ## 
 ## DTx values:
@@ -602,19 +614,25 @@
 ## DFOP 5.58 18.5     5.58
 ## 
 ## Representative half-life:
-## [1] 3.987308</code></pre>
+## [1] 3.99</code></pre>
 </div>
 <div id="example-on-page-12-lower-panel" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-12-lower-panel" class="anchor"></a>Example on page 12, lower panel</h2>
-<div class="sourceCode" id="cb71"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb71-1" title="1">p12b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p12b"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb66"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb66-1" title="1">p12b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p12b"</span>]])</a></code></pre></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in qt(alpha/2, rdf): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in qt(1 - alpha/2, rdf): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
+## finite result is doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb75"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb75-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p12b)</a></code></pre></div>
+<div class="sourceCode" id="cb76"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb76-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p12b)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p>
-<div class="sourceCode" id="cb76"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb76-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p12b)</a></code></pre></div>
+<div class="sourceCode" id="cb77"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb77-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p12b)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 58.90242 19.06353 58.90242 
@@ -624,22 +642,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)   Lower    Upper
-## parent_0       97.6840 5.36e-05 86.3205 109.0475
-## k_parent_sink   0.0589 9.87e-04  0.0432   0.0803
+##               Estimate  Pr(&gt;t)   Lower    Upper
+## parent_0       97.6840 0.00039 85.9388 109.4292
+## k_parent_sink   0.0589 0.00261  0.0431   0.0805
+## sigma           3.4323 0.04356 -1.2377   8.1023
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)   Lower  Upper
-## parent_0              95.523 0.000386 84.0963 106.95
-## k__iore_parent_sink    0.333 0.170886  0.0103  10.80
-## N_parent               0.568 0.054881 -0.3161   1.45
+##                     Estimate Pr(&gt;t)     Lower  Upper
+## parent_0              95.523 0.0055 74.539157 116.51
+## k__iore_parent_sink    0.333 0.1433  0.000717 154.57
+## N_parent               0.568 0.0677 -0.989464   2.13
+## sigma                  1.953 0.0975 -5.893100   9.80
 ## 
 ## $DFOP
 ##          Estimate Pr(&gt;t) Lower Upper
-## parent_0  97.6840     NA    NA    NA
-## k1         0.0589     NA    NA    NA
-## k2         0.0589     NA    NA    NA
-## g          0.6902     NA    NA    NA
+## parent_0  97.6840    NaN   NaN   NaN
+## k1         0.0589    NaN    NA    NA
+## k2         0.0589    NaN    NA    NA
+## g          0.6902    NaN    NA    NA
+## sigma      3.4323    NaN   NaN   NaN
 ## 
 ## 
 ## DTx values:
@@ -649,19 +670,21 @@
 ## DFOP 11.8 39.1    11.80
 ## 
 ## Representative half-life:
-## [1] 9.461912</code></pre>
+## [1] 9.46</code></pre>
 </div>
 <div id="example-on-page-13" class="section level2">
 <h2 class="hasAnchor">
 <a href="#example-on-page-13" class="anchor"></a>Example on page 13</h2>
-<div class="sourceCode" id="cb78"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb78-1" title="1">p13 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p13"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb79"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb79-1" title="1">p13 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p13"</span>]])</a></code></pre></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
+## finite result is doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb82"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb82-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p13)</a></code></pre></div>
+<div class="sourceCode" id="cb85"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb85-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p13)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p>
-<div class="sourceCode" id="cb83"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb83-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p13)</a></code></pre></div>
+<div class="sourceCode" id="cb86"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb86-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p13)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 174.5971 142.3951 174.5971 
@@ -671,22 +694,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)   Lower    Upper
-## parent_0      92.73500 1.45e-17 89.3891 96.08094
-## k_parent_sink  0.00258 2.63e-09  0.0022  0.00303
+##               Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0      92.73500 5.99e-17 89.61936 95.85065
+## k_parent_sink  0.00258 2.42e-09  0.00223  0.00299
+## sigma          3.41172 7.07e-05  2.05455  4.76888
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)    Lower Upper
-## parent_0             91.6016 2.93e-16 88.08711 95.12
-## k__iore_parent_sink   0.0396 2.81e-01  0.00102  1.53
-## N_parent              0.3541 1.97e-01 -0.51943  1.23
+##                     Estimate   Pr(&gt;t)    Lower  Upper
+## parent_0             91.6016 6.34e-16 88.53086 94.672
+## k__iore_parent_sink   0.0396 2.36e-01  0.00207  0.759
+## N_parent              0.3541 1.46e-01 -0.35153  1.060
+## sigma                 3.0811 9.64e-05  1.84296  4.319
 ## 
 ## $DFOP
-##          Estimate Pr(&gt;t) Lower Upper
-## parent_0 92.73500     NA    NA    NA
-## k1        0.00258     NA    NA    NA
-## k2        0.00258     NA    NA    NA
-## g         0.00442     NA    NA    NA
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 92.73500 9.25e-15 8.95e+01 9.59e+01
+## k1        0.00258 4.28e-01 1.70e-08 3.92e+02
+## k2        0.00258 3.69e-08 2.20e-03 3.03e-03
+## g         0.00442 5.00e-01       NA       NA
+## sigma     3.41172 1.35e-04 2.02e+00 4.80e+00
 ## 
 ## 
 ## DTx values:
@@ -696,20 +722,22 @@
 ## DFOP  269  892      269
 ## 
 ## Representative half-life:
-## [1] 168.5123</code></pre>
+## [1] 168.51</code></pre>
 </div>
 </div>
 <div id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="section level1">
 <h1 class="hasAnchor">
 <a href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="anchor"></a>DT50 not observed in the study and DFOP problems in PestDF</h1>
-<div class="sourceCode" id="cb85"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb85-1" title="1">p14 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p14"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb88"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb88-1" title="1">p14 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p14"</span>]])</a></code></pre></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
+## finite result is doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb89"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb89-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p14)</a></code></pre></div>
+<div class="sourceCode" id="cb94"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb94-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p14)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p>
-<div class="sourceCode" id="cb90"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb90-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p14)</a></code></pre></div>
+<div class="sourceCode" id="cb95"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb95-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p14)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 48.43249 28.67746 27.26248 
@@ -720,21 +748,24 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0      99.47124 1.71e-31 98.37313 1.01e+02
-## k_parent_sink  0.00279 2.22e-15  0.00255 3.05e-03
+## parent_0      99.47124 2.06e-30 98.42254 1.01e+02
+## k_parent_sink  0.00279 3.75e-15  0.00256 3.04e-03
+## sigma          1.55616 3.81e-06  1.03704 2.08e+00
 ## 
 ## $IORE
-##                     Estimate Pr(&gt;t)    Lower    Upper
-## parent_0            1.00e+02     NA 9.93e+01 1.01e+02
-## k__iore_parent_sink 9.44e-08     NA 6.81e-11 1.31e-04
-## N_parent            3.31e+00     NA 1.69e+00 4.93e+00
+##                     Estimate Pr(&gt;t) Lower Upper
+## parent_0            1.00e+02     NA   NaN   NaN
+## k__iore_parent_sink 9.44e-08     NA   NaN   NaN
+## N_parent            3.31e+00     NA   NaN   NaN
+## sigma               1.20e+00     NA 0.796   1.6
 ## 
 ## $DFOP
-##          Estimate   Pr(&gt;t) Lower Upper
-## parent_0 1.00e+02 2.70e-28    NA    NA
-## k1       9.53e-03 3.39e-01    NA    NA
-## k2       7.29e-12 5.00e-01    NA    NA
-## g        3.98e-01 3.92e-01    NA    NA
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 1.00e+02 2.96e-28 99.40280 101.2768
+## k1       9.53e-03 1.20e-01  0.00638   0.0143
+## k2       7.29e-12 5.00e-01  0.00000      Inf
+## g        3.98e-01 2.19e-01  0.30481   0.4998
+## sigma    1.17e+00 7.68e-06  0.77406   1.5610
 ## 
 ## 
 ## DTx values:
@@ -744,20 +775,23 @@
 ## DFOP 2.54e+10 2.46e+11 9.51e+10
 ## 
 ## Representative half-life:
-## [1] 6697.437</code></pre>
+## [1] 6697.44</code></pre>
 <p>The slower rate constant reported by PestDF is negative, which is not physically realistic, and not possible in mkin. The other fits give the same results in mkin and PestDF.</p>
 </div>
 <div id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="section level1">
 <h1 class="hasAnchor">
 <a href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="anchor"></a>N is less than 1 and DFOP fraction parameter is below zero</h1>
-<div class="sourceCode" id="cb92"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb92-1" title="1">p15a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p15a"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+<div class="sourceCode" id="cb97"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb97-1" title="1">p15a &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p15a"</span>]])</a></code></pre></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
+## finite result is doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb96"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb96-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p15a)</a></code></pre></div>
+<div class="sourceCode" id="cb104"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb104-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p15a)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p>
-<div class="sourceCode" id="cb97"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb97-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p15a)</a></code></pre></div>
+<div class="sourceCode" id="cb105"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb105-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p15a)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 245.5248 135.0132 245.5248 
@@ -767,22 +801,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0      97.96751 4.98e-16 94.03829 101.8967
-## k_parent_sink  0.00952 5.24e-09  0.00813   0.0112
+##               Estimate   Pr(&gt;t)    Lower   Upper
+## parent_0      97.96751 2.00e-15 94.32049 101.615
+## k_parent_sink  0.00952 4.93e-09  0.00824   0.011
+## sigma          4.18778 1.28e-04  2.44588   5.930
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)   Lower  Upper
-## parent_0              95.874 8.30e-16 92.5802 99.167
-## k__iore_parent_sink    0.629 2.39e-01  0.0316 12.519
-## N_parent               0.000 5.00e-01 -0.7219  0.722
+##                     Estimate   Pr(&gt;t)  Lower  Upper
+## parent_0              95.874 2.94e-15 92.937 98.811
+## k__iore_parent_sink    0.629 2.11e-01  0.044  8.982
+## N_parent               0.000 5.00e-01 -0.642  0.642
+## sigma                  3.105 1.78e-04  1.795  4.416
 ## 
 ## $DFOP
-##          Estimate Pr(&gt;t) Lower Upper
-## parent_0 97.96752     NA    NA    NA
-## k1        0.00952     NA    NA    NA
-## k2        0.00952     NA    NA    NA
-## g         0.17247     NA    NA    NA
+##          Estimate   Pr(&gt;t)    Lower    Upper
+## parent_0 97.96752 2.85e-13 94.21914 101.7159
+## k1        0.00952 6.80e-02  0.00277   0.0327
+## k2        0.00952 3.82e-06  0.00902   0.0100
+## g         0.17247      NaN       NA       NA
+## sigma     4.18778 2.50e-04  2.39747   5.9781
 ## 
 ## 
 ## DTx values:
@@ -792,15 +829,17 @@
 ## DFOP 72.8  242     72.8
 ## 
 ## Representative half-life:
-## [1] 41.32749</code></pre>
-<div class="sourceCode" id="cb99"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb99-1" title="1">p15b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p15b"</span>]])</a></code></pre></div>
-<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.</code></pre>
+## [1] 41.33</code></pre>
+<div class="sourceCode" id="cb107"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb107-1" title="1">p15b &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p15b"</span>]])</a></code></pre></div>
+<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre>
+<pre><code>## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
+## finite result is doubtful</code></pre>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The half-life obtained from the IORE model may be used</code></pre>
-<div class="sourceCode" id="cb103"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb103-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p15b)</a></code></pre></div>
+<div class="sourceCode" id="cb113"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb113-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p15b)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p>
-<div class="sourceCode" id="cb104"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb104-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p15b)</a></code></pre></div>
+<div class="sourceCode" id="cb114"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb114-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p15b)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 106.91629  68.55574 106.91629 
@@ -811,21 +850,24 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0      1.01e+02 4.99e-18 98.12761 1.04e+02
-## k_parent_sink 4.86e-03 1.76e-10  0.00432 5.46e-03
+## parent_0      1.01e+02 3.06e-17 98.31594 1.03e+02
+## k_parent_sink 4.86e-03 2.48e-10  0.00435 5.42e-03
+## sigma         2.76e+00 1.28e-04  1.61402 3.91e+00
 ## 
 ## $IORE
-##                     Estimate   Pr(&gt;t)    Lower Upper
-## parent_0               99.83 4.49e-17 97.19753 102.5
-## k__iore_parent_sink     0.38 3.41e-01  0.00206  70.0
-## N_parent                0.00 5.00e-01 -1.20105   1.2
+##                     Estimate   Pr(&gt;t)    Lower  Upper
+## parent_0               99.83 1.81e-16 97.51349 102.14
+## k__iore_parent_sink     0.38 3.22e-01  0.00352  41.05
+## N_parent                0.00 5.00e-01 -1.07695   1.08
+## sigma                   2.21 2.57e-04  1.23245   3.19
 ## 
 ## $DFOP
-##          Estimate Pr(&gt;t) Lower Upper
-## parent_0 1.01e+02     NA    NA    NA
-## k1       4.86e-03     NA    NA    NA
-## k2       4.86e-03     NA    NA    NA
-## g        1.50e-01     NA    NA    NA
+##          Estimate Pr(&gt;t)    Lower    Upper
+## parent_0 1.01e+02     NA 9.82e+01 1.04e+02
+## k1       4.86e-03     NA 6.75e-04 3.49e-02
+## k2       4.86e-03     NA 3.37e-03 6.99e-03
+## g        1.50e-01     NA       NA       NA
+## sigma    2.76e+00     NA 1.58e+00 3.94e+00
 ## 
 ## 
 ## DTx values:
@@ -835,20 +877,20 @@
 ## DFOP  143  474    143.0
 ## 
 ## Representative half-life:
-## [1] 71.18014</code></pre>
+## [1] 71.18</code></pre>
 <p>In mkin, only the IORE fit is affected (deemed unrealistic), as the fraction parameter of the DFOP model is restricted to the interval between 0 and 1 in mkin. The SFO fits give the same results for both mkin and PestDF.</p>
 </div>
 <div id="the-dfop-fraction-parameter-is-greater-than-1" class="section level1">
 <h1 class="hasAnchor">
 <a href="#the-dfop-fraction-parameter-is-greater-than-1" class="anchor"></a>The DFOP fraction parameter is greater than 1</h1>
-<div class="sourceCode" id="cb106"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb106-1" title="1">p16 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p16"</span>]])</a></code></pre></div>
+<div class="sourceCode" id="cb116"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb116-1" title="1">p16 &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p16"</span>]])</a></code></pre></div>
 <pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
 <pre><code>## The representative half-life of the IORE model is longer than the one corresponding</code></pre>
 <pre><code>## to the terminal degradation rate found with the DFOP model.</code></pre>
 <pre><code>## The representative half-life obtained from the DFOP model may be used</code></pre>
-<div class="sourceCode" id="cb111"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb111-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p16)</a></code></pre></div>
+<div class="sourceCode" id="cb121"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb121-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p16)</a></code></pre></div>
 <p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p>
-<div class="sourceCode" id="cb112"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb112-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p16)</a></code></pre></div>
+<div class="sourceCode" id="cb122"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb122-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p16)</a></code></pre></div>
 <pre><code>## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3831.804 2062.008 1550.980 
@@ -858,22 +900,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(&gt;t)  Lower  Upper
-## parent_0        71.953 3.92e-14 61.087 82.819
-## k_parent_sink    0.159 2.27e-06  0.111  0.229
+##               Estimate   Pr(&gt;t)  Lower Upper
+## parent_0        71.953 2.33e-13 60.509 83.40
+## k_parent_sink    0.159 4.86e-05  0.102  0.25
+## sigma           11.302 1.25e-08  8.308 14.30
 ## 
 ## $IORE
 ##                     Estimate   Pr(&gt;t)    Lower    Upper
-## parent_0            8.74e+01 1.74e-16 7.71e+01 97.70701
-## k__iore_parent_sink 4.55e-04 2.28e-01 3.01e-05  0.00688
-## N_parent            2.70e+00 1.87e-08 1.97e+00  3.42611
+## parent_0            8.74e+01 2.48e-16 7.72e+01 97.52972
+## k__iore_parent_sink 4.55e-04 2.16e-01 3.48e-05  0.00595
+## N_parent            2.70e+00 1.21e-08 1.99e+00  3.40046
+## sigma               8.29e+00 1.61e-08 6.09e+00 10.49062
 ## 
 ## $DFOP
-##          Estimate Pr(&gt;t)   Lower  Upper
-## parent_0  88.5333     NA 79.3673 97.699
-## k1        18.5561     NA  0.0000    Inf
-## k2         0.0776     NA  0.0471  0.128
-## g          0.4733     NA  0.3138  0.639
+##          Estimate   Pr(&gt;t)   Lower  Upper
+## parent_0  88.5333 7.40e-18 79.9836 97.083
+## k1        18.5561 5.00e-01  0.0000    Inf
+## k2         0.0776 1.41e-05  0.0518  0.116
+## g          0.4733 1.41e-09  0.3674  0.582
+## sigma      7.1902 2.11e-08  5.2785  9.102
 ## 
 ## 
 ## DTx values:
@@ -883,7 +928,7 @@
 ## DFOP 0.67 21.4     8.93
 ## 
 ## Representative half-life:
-## [1] 8.932679</code></pre>
+## [1] 8.93</code></pre>
 <p>In PestDF, the DFOP fit seems to have stuck in a local minimum, as mkin finds a solution with a much lower <span class="math inline">\(\chi^2\)</span> error level. As the half-life from the slower rate constant of the DFOP model is larger than the IORE derived half-life, the NAFTA recommendation obtained with mkin is to use the DFOP representative half-life of 8.9 days.</p>
 </div>
 <div id="conclusions" class="section level1">
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png
index 4cf9c8ea..d0f89858 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png
index c1f61bab..596a33b2 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png
index 2747b2d6..fa8621e7 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png
index 32b3bf29..aac3600b 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
index 8b8ea5aa..cb52aecd 100644
--- a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
+++ b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png
diff --git a/docs/articles/web_only/benchmarks.html b/docs/articles/web_only/benchmarks.html
index eacecc2f..f71659be 100644
--- a/docs/articles/web_only/benchmarks.html
+++ b/docs/articles/web_only/benchmarks.html
@@ -88,7 +88,7 @@
       <h1>Benchmark timings for mkin on various systems</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2019-07-05</h4>
+            <h4 class="date">2019-07-09</h4>
       
       
       <div class="hidden name"><code>benchmarks.Rmd</code></div>
@@ -116,17 +116,8 @@
 <div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" title="1"><span class="co"># Parent only</span></a>
 <a class="sourceLine" id="cb2-2" title="2">t1 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span>), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(FOCUS_<span class="dv">2006</span>_C, FOCUS_<span class="dv">2006</span>_D)))[[<span class="st">"elapsed"</span>]]</a>
 <a class="sourceLine" id="cb2-3" title="3">t2 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>, <span class="st">"HS"</span>), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(FOCUS_<span class="dv">2006</span>_C, FOCUS_<span class="dv">2006</span>_D), <span class="dt">error_model =</span> <span class="st">"tc"</span>))[[<span class="st">"elapsed"</span>]]</a></code></pre></div>
-<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
-## false convergence (8)
-
-## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
-## false convergence (8)
-
-## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
-## false convergence (8)
-
-## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
-## false convergence (8)</code></pre>
+<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation did not converge:
+## iteration limit reached without convergence (10)</code></pre>
 <div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" title="1"><span class="co"># One metabolite</span></a>
 <a class="sourceLine" id="cb4-2" title="2">SFO_SFO &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(</a>
 <a class="sourceLine" id="cb4-3" title="3">  <span class="dt">parent =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"m1"</span>),</a>
@@ -140,124 +131,149 @@
 <a class="sourceLine" id="cb8-2" title="2">  <span class="dt">parent =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),</a>
 <a class="sourceLine" id="cb8-3" title="3">  <span class="dt">m1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>))</a></code></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
-<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" title="1">t3 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_SFO, FOMC_SFO, DFOP_SFO), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(FOCUS_<span class="dv">2006</span>_D)))[[<span class="st">"elapsed"</span>]]</a>
-<a class="sourceLine" id="cb10-2" title="2">t4 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_SFO, FOMC_SFO, DFOP_SFO), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/subset">subset</a></span>(FOCUS_<span class="dv">2006</span>_D, value <span class="op">!=</span><span class="st"> </span><span class="dv">0</span>)), <span class="dt">error_model =</span> <span class="st">"tc"</span>))[[<span class="st">"elapsed"</span>]]</a>
-<a class="sourceLine" id="cb10-3" title="3">t5 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_SFO, FOMC_SFO, DFOP_SFO), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(FOCUS_<span class="dv">2006</span>_D), <span class="dt">error_model =</span> <span class="st">"obs"</span>))[[<span class="st">"elapsed"</span>]]</a>
-<a class="sourceLine" id="cb10-4" title="4"></a>
-<a class="sourceLine" id="cb10-5" title="5"><span class="co"># Two metabolites, synthetic data</span></a>
-<a class="sourceLine" id="cb10-6" title="6">m_synth_SFO_lin &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">parent =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M1"</span>),</a>
-<a class="sourceLine" id="cb10-7" title="7">                           <span class="dt">M1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M2"</span>),</a>
-<a class="sourceLine" id="cb10-8" title="8">                           <span class="dt">M2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),</a>
-<a class="sourceLine" id="cb10-9" title="9">                           <span class="dt">use_of_ff =</span> <span class="st">"max"</span>, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb10-10" title="10"></a>
-<a class="sourceLine" id="cb10-11" title="11">m_synth_DFOP_par &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">parent =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"DFOP"</span>, <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"M1"</span>, <span class="st">"M2"</span>)),</a>
-<a class="sourceLine" id="cb10-12" title="12">                           <span class="dt">M1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),</a>
-<a class="sourceLine" id="cb10-13" title="13">                           <span class="dt">M2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),</a>
-<a class="sourceLine" id="cb10-14" title="14">                           <span class="dt">use_of_ff =</span> <span class="st">"max"</span>, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
-<a class="sourceLine" id="cb10-15" title="15"></a>
-<a class="sourceLine" id="cb10-16" title="16">SFO_lin_a &lt;-<span class="st"> </span>synthetic_data_for_UBA_<span class="dv">2014</span>[[<span class="dv">1</span>]]<span class="op">$</span>data</a>
-<a class="sourceLine" id="cb10-17" title="17"></a>
-<a class="sourceLine" id="cb10-18" title="18">DFOP_par_c &lt;-<span class="st"> </span>synthetic_data_for_UBA_<span class="dv">2014</span>[[<span class="dv">12</span>]]<span class="op">$</span>data</a>
-<a class="sourceLine" id="cb10-19" title="19"></a>
-<a class="sourceLine" id="cb10-20" title="20">t6 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_SFO_lin), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_lin_a)))[<span class="st">"elapsed"</span>]</a>
-<a class="sourceLine" id="cb10-21" title="21">t7 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_DFOP_par), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(DFOP_par_c)))[<span class="st">"elapsed"</span>]</a>
-<a class="sourceLine" id="cb10-22" title="22"></a>
-<a class="sourceLine" id="cb10-23" title="23">t8 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_SFO_lin), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_lin_a), <span class="dt">error_model =</span> <span class="st">"tc"</span>))[<span class="st">"elapsed"</span>]</a></code></pre></div>
-<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
-## false convergence (8)</code></pre>
-<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb12-1" title="1">t9 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_DFOP_par), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(DFOP_par_c), <span class="dt">error_model =</span> <span class="st">"tc"</span>))[<span class="st">"elapsed"</span>]</a>
-<a class="sourceLine" id="cb12-2" title="2"></a>
-<a class="sourceLine" id="cb12-3" title="3">t10 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_SFO_lin), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_lin_a), <span class="dt">error_model =</span> <span class="st">"obs"</span>))[<span class="st">"elapsed"</span>]</a>
-<a class="sourceLine" id="cb12-4" title="4">t11 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_DFOP_par), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(DFOP_par_c), <span class="dt">error_model =</span> <span class="st">"obs"</span>))[<span class="st">"elapsed"</span>]</a></code></pre></div>
-<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
-## false convergence (8)</code></pre>
-<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb14-1" title="1">mkin_benchmarks[system_string, <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/paste">paste0</a></span>(<span class="st">"t"</span>, <span class="dv">1</span><span class="op">:</span><span class="dv">11</span>)] &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11)</a>
-<a class="sourceLine" id="cb14-2" title="2">mkin_benchmarks</a></code></pre></div>
+<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" title="1">t3 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_SFO, FOMC_SFO, DFOP_SFO), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(FOCUS_<span class="dv">2006</span>_D)))[[<span class="st">"elapsed"</span>]]</a></code></pre></div>
+<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
+## Observations with value of zero were removed from the data</code></pre>
+<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
+## Observations with value of zero were removed from the data
+
+## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
+## Observations with value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1">t4 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_SFO, FOMC_SFO, DFOP_SFO), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/subset">subset</a></span>(FOCUS_<span class="dv">2006</span>_D, value <span class="op">!=</span><span class="st"> </span><span class="dv">0</span>)), <span class="dt">error_model =</span> <span class="st">"tc"</span>))[[<span class="st">"elapsed"</span>]]</a>
+<a class="sourceLine" id="cb13-2" title="2">t5 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_SFO, FOMC_SFO, DFOP_SFO), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(FOCUS_<span class="dv">2006</span>_D), <span class="dt">error_model =</span> <span class="st">"obs"</span>))[[<span class="st">"elapsed"</span>]]</a></code></pre></div>
+<pre><code>## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
+## Observations with value of zero were removed from the data
+
+## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
+## Observations with value of zero were removed from the data
+
+## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
+## Observations with value of zero were removed from the data</code></pre>
+<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb15-1" title="1"><span class="co"># Two metabolites, synthetic data</span></a>
+<a class="sourceLine" id="cb15-2" title="2">m_synth_SFO_lin &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">parent =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M1"</span>),</a>
+<a class="sourceLine" id="cb15-3" title="3">                           <span class="dt">M1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>, <span class="st">"M2"</span>),</a>
+<a class="sourceLine" id="cb15-4" title="4">                           <span class="dt">M2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),</a>
+<a class="sourceLine" id="cb15-5" title="5">                           <span class="dt">use_of_ff =</span> <span class="st">"max"</span>, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
+<a class="sourceLine" id="cb15-6" title="6"></a>
+<a class="sourceLine" id="cb15-7" title="7">m_synth_DFOP_par &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(<span class="dt">parent =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"DFOP"</span>, <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"M1"</span>, <span class="st">"M2"</span>)),</a>
+<a class="sourceLine" id="cb15-8" title="8">                           <span class="dt">M1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),</a>
+<a class="sourceLine" id="cb15-9" title="9">                           <span class="dt">M2 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"SFO"</span>),</a>
+<a class="sourceLine" id="cb15-10" title="10">                           <span class="dt">use_of_ff =</span> <span class="st">"max"</span>, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
+<a class="sourceLine" id="cb15-11" title="11"></a>
+<a class="sourceLine" id="cb15-12" title="12">SFO_lin_a &lt;-<span class="st"> </span>synthetic_data_for_UBA_<span class="dv">2014</span>[[<span class="dv">1</span>]]<span class="op">$</span>data</a>
+<a class="sourceLine" id="cb15-13" title="13"></a>
+<a class="sourceLine" id="cb15-14" title="14">DFOP_par_c &lt;-<span class="st"> </span>synthetic_data_for_UBA_<span class="dv">2014</span>[[<span class="dv">12</span>]]<span class="op">$</span>data</a>
+<a class="sourceLine" id="cb15-15" title="15"></a>
+<a class="sourceLine" id="cb15-16" title="16">t6 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_SFO_lin), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_lin_a)))[<span class="st">"elapsed"</span>]</a>
+<a class="sourceLine" id="cb15-17" title="17">t7 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_DFOP_par), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(DFOP_par_c)))[<span class="st">"elapsed"</span>]</a>
+<a class="sourceLine" id="cb15-18" title="18"></a>
+<a class="sourceLine" id="cb15-19" title="19">t8 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_SFO_lin), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_lin_a), <span class="dt">error_model =</span> <span class="st">"tc"</span>))[<span class="st">"elapsed"</span>]</a>
+<a class="sourceLine" id="cb15-20" title="20">t9 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_DFOP_par), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(DFOP_par_c), <span class="dt">error_model =</span> <span class="st">"tc"</span>))[<span class="st">"elapsed"</span>]</a>
+<a class="sourceLine" id="cb15-21" title="21"></a>
+<a class="sourceLine" id="cb15-22" title="22">t10 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_SFO_lin), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(SFO_lin_a), <span class="dt">error_model =</span> <span class="st">"obs"</span>))[<span class="st">"elapsed"</span>]</a>
+<a class="sourceLine" id="cb15-23" title="23">t11 &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/system.time">system.time</a></span>(<span class="kw">mmkin_bench</span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(m_synth_DFOP_par), <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(DFOP_par_c), <span class="dt">error_model =</span> <span class="st">"obs"</span>))[<span class="st">"elapsed"</span>]</a>
+<a class="sourceLine" id="cb15-24" title="24"></a>
+<a class="sourceLine" id="cb15-25" title="25">mkin_benchmarks[system_string, <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/paste">paste0</a></span>(<span class="st">"t"</span>, <span class="dv">1</span><span class="op">:</span><span class="dv">11</span>)] &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11)</a>
+<a class="sourceLine" id="cb15-26" title="26">mkin_benchmarks</a></code></pre></div>
 <pre><code>##                                                                                                       CPU
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 AMD Ryzen 7 1700 Eight-Core Processor
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 AMD Ryzen 7 1700 Eight-Core Processor
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 AMD Ryzen 7 1700 Eight-Core Processor
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 AMD Ryzen 7 1700 Eight-Core Processor
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 AMD Ryzen 7 1700 Eight-Core Processor
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 AMD Ryzen 7 1700 Eight-Core Processor
 ##                                                                        OS
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 Linux
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 Linux
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 Linux
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 Linux
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 Linux
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 Linux
 ##                                                                         mkin
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 0.9.48.1
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 0.9.49.1
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 0.9.49.2
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 0.9.49.3
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 0.9.49.4
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 0.9.49.6
 ##                                                                        t1
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.107
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.610
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 8.184
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 7.064
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.296
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 5.936
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 5.826
 ##                                                                         t2
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 10.105
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 11.019
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 22.889
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 12.558
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 21.239
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 20.545
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 36.053
 ##                                                                        t3
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.415
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.764
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.649
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.786
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 4.510
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.446
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 4.452
 ##                                                                         t4
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 13.228
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 14.347
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 13.789
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  8.461
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 13.805
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 15.335
-##                                                                        t5
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 8.511
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 6.395
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 5.675
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.386
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 6.002
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 30.603
+##                                                                         t5
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1  9.495
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1  6.395
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  5.675
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3  7.386
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  6.002
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 10.465
 ##                                                                        t6
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 2.368
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 2.623
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 2.542
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 2.723
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 2.643
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 2.635
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 2.595
 ##                                                                        t7
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1  4.12
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 4.587
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.128
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.478
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 4.374
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.259
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 4.202
 ##                                                                        t8
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 6.357
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 7.525
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.632
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.862
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3  7.02
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.737
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 7.726
 ##                                                                         t9
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1  15.42
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 16.621
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1  8.171
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  7.618
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 11.124
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  7.763
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 23.042
 ##                                                                       t10
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 7.868
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 8.576
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 3.676
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 3.579
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 5.388
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 3.427
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 18.26
 ##                                                                        t11
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 28.858
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 31.267
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1  5.636
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  5.574
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3  7.365
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  5.626</code></pre>
-<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb16-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/save">save</a></span>(mkin_benchmarks, <span class="dt">file =</span> <span class="st">"~/git/mkin/vignettes/mkin_benchmarks.rda"</span>)</a></code></pre></div>
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  5.626
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.6 12.106</code></pre>
+<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb17-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/save">save</a></span>(mkin_benchmarks, <span class="dt">file =</span> <span class="st">"~/git/mkin/vignettes/mkin_benchmarks.rda"</span>)</a></code></pre></div>
 </div>
   </div>
 
diff --git a/docs/articles/web_only/compiled_models.html b/docs/articles/web_only/compiled_models.html
index ca883f17..0bb564ad 100644
--- a/docs/articles/web_only/compiled_models.html
+++ b/docs/articles/web_only/compiled_models.html
@@ -88,7 +88,7 @@
       <h1>Performance benefit by using compiled model definitions in mkin</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2019-07-05</h4>
+            <h4 class="date">2019-07-09</h4>
       
       
       <div class="hidden name"><code>compiled_models.Rmd</code></div>
@@ -128,45 +128,99 @@
 <a class="sourceLine" id="cb5-15" title="15">  <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(<span class="st">"R package rbenchmark is not available"</span>)</a>
 <a class="sourceLine" id="cb5-16" title="16">}</a></code></pre></div>
 <pre><code>## Lade nötiges Paket: rbenchmark</code></pre>
+<pre><code>## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve",
+## use_compiled = FALSE, : Observations with value of zero were removed from
+## the data</code></pre>
+<pre><code>## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet =
+## TRUE): Observations with value of zero were removed from the data</code></pre>
+<pre><code>## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet
+## = TRUE): Observations with value of zero were removed from the data</code></pre>
+<pre><code>## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve",
+## use_compiled = FALSE, : Observations with value of zero were removed from
+## the data
+
+## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve",
+## use_compiled = FALSE, : Observations with value of zero were removed from
+## the data
+
+## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve",
+## use_compiled = FALSE, : Observations with value of zero were removed from
+## the data</code></pre>
+<pre><code>## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet =
+## TRUE): Observations with value of zero were removed from the data
+
+## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet =
+## TRUE): Observations with value of zero were removed from the data
+
+## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet =
+## TRUE): Observations with value of zero were removed from the data</code></pre>
+<pre><code>## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet
+## = TRUE): Observations with value of zero were removed from the data
+
+## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet
+## = TRUE): Observations with value of zero were removed from the data
+
+## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet
+## = TRUE): Observations with value of zero were removed from the data</code></pre>
 <pre><code>##                    test replications elapsed relative user.self sys.self
-## 3     deSolve, compiled            3   2.147    1.000     2.145        0
-## 1 deSolve, not compiled            3  12.653    5.893    12.646        0
-## 2      Eigenvalue based            3   2.690    1.253     2.688        0
+## 3     deSolve, compiled            3   3.127    1.000     3.125        0
+## 1 deSolve, not compiled            3  28.337    9.062    28.322        0
+## 2      Eigenvalue based            3   4.320    1.382     4.317        0
 ##   user.child sys.child
 ## 3          0         0
 ## 1          0         0
 ## 2          0         0</code></pre>
-<p>We see that using the compiled model is by a factor of around 6 faster than using the R version with the default ode solver, and it is even faster than the Eigenvalue based solution implemented in R which does not need iterative solution of the ODEs.</p>
+<p>We see that using the compiled model is by a factor of around 9 faster than using the R version with the default ode solver, and it is even faster than the Eigenvalue based solution implemented in R which does not need iterative solution of the ODEs.</p>
 </div>
 <div id="model-that-can-not-be-solved-with-eigenvalues" class="section level2">
 <h2 class="hasAnchor">
 <a href="#model-that-can-not-be-solved-with-eigenvalues" class="anchor"></a>Model that can not be solved with Eigenvalues</h2>
 <p>This evaluation is also taken from the example section of mkinfit.</p>
-<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" title="1"><span class="cf">if</span> (<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/library">require</a></span>(rbenchmark)) {</a>
-<a class="sourceLine" id="cb8-2" title="2">  FOMC_SFO &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(</a>
-<a class="sourceLine" id="cb8-3" title="3">    <span class="dt">parent =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),</a>
-<a class="sourceLine" id="cb8-4" title="4">    <span class="dt">m1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>( <span class="st">"SFO"</span>))</a>
-<a class="sourceLine" id="cb8-5" title="5"></a>
-<a class="sourceLine" id="cb8-6" title="6">  b<span class="fl">.2</span> &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/rbenchmark/topics/benchmark">benchmark</a></span>(</a>
-<a class="sourceLine" id="cb8-7" title="7">    <span class="st">"deSolve, not compiled"</span> =<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(FOMC_SFO, FOCUS_<span class="dv">2006</span>_D,</a>
-<a class="sourceLine" id="cb8-8" title="8">                                      <span class="dt">use_compiled =</span> <span class="ot">FALSE</span>, <span class="dt">quiet =</span> <span class="ot">TRUE</span>),</a>
-<a class="sourceLine" id="cb8-9" title="9">    <span class="st">"deSolve, compiled"</span> =<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(FOMC_SFO, FOCUS_<span class="dv">2006</span>_D, <span class="dt">quiet =</span> <span class="ot">TRUE</span>),</a>
-<a class="sourceLine" id="cb8-10" title="10">    <span class="dt">replications =</span> <span class="dv">3</span>)</a>
-<a class="sourceLine" id="cb8-11" title="11">  <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(b<span class="fl">.2</span>)</a>
-<a class="sourceLine" id="cb8-12" title="12">  factor_FOMC_SFO &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/Round">round</a></span>(b<span class="fl">.2</span>[<span class="st">"1"</span>, <span class="st">"relative"</span>])</a>
-<a class="sourceLine" id="cb8-13" title="13">} <span class="cf">else</span> {</a>
-<a class="sourceLine" id="cb8-14" title="14">  factor_FOMC_SFO &lt;-<span class="st"> </span><span class="ot">NA</span></a>
-<a class="sourceLine" id="cb8-15" title="15">  <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(<span class="st">"R package benchmark is not available"</span>)</a>
-<a class="sourceLine" id="cb8-16" title="16">}</a></code></pre></div>
+<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb14-1" title="1"><span class="cf">if</span> (<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/library">require</a></span>(rbenchmark)) {</a>
+<a class="sourceLine" id="cb14-2" title="2">  FOMC_SFO &lt;-<span class="st"> </span><span class="kw"><a href="../../reference/mkinmod.html">mkinmod</a></span>(</a>
+<a class="sourceLine" id="cb14-3" title="3">    <span class="dt">parent =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>(<span class="st">"FOMC"</span>, <span class="st">"m1"</span>),</a>
+<a class="sourceLine" id="cb14-4" title="4">    <span class="dt">m1 =</span> <span class="kw"><a href="../../reference/mkinsub.html">mkinsub</a></span>( <span class="st">"SFO"</span>))</a>
+<a class="sourceLine" id="cb14-5" title="5"></a>
+<a class="sourceLine" id="cb14-6" title="6">  b<span class="fl">.2</span> &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/rbenchmark/topics/benchmark">benchmark</a></span>(</a>
+<a class="sourceLine" id="cb14-7" title="7">    <span class="st">"deSolve, not compiled"</span> =<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(FOMC_SFO, FOCUS_<span class="dv">2006</span>_D,</a>
+<a class="sourceLine" id="cb14-8" title="8">                                      <span class="dt">use_compiled =</span> <span class="ot">FALSE</span>, <span class="dt">quiet =</span> <span class="ot">TRUE</span>),</a>
+<a class="sourceLine" id="cb14-9" title="9">    <span class="st">"deSolve, compiled"</span> =<span class="st"> </span><span class="kw"><a href="../../reference/mkinfit.html">mkinfit</a></span>(FOMC_SFO, FOCUS_<span class="dv">2006</span>_D, <span class="dt">quiet =</span> <span class="ot">TRUE</span>),</a>
+<a class="sourceLine" id="cb14-10" title="10">    <span class="dt">replications =</span> <span class="dv">3</span>)</a>
+<a class="sourceLine" id="cb14-11" title="11">  <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(b<span class="fl">.2</span>)</a>
+<a class="sourceLine" id="cb14-12" title="12">  factor_FOMC_SFO &lt;-<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/Round">round</a></span>(b<span class="fl">.2</span>[<span class="st">"1"</span>, <span class="st">"relative"</span>])</a>
+<a class="sourceLine" id="cb14-13" title="13">} <span class="cf">else</span> {</a>
+<a class="sourceLine" id="cb14-14" title="14">  factor_FOMC_SFO &lt;-<span class="st"> </span><span class="ot">NA</span></a>
+<a class="sourceLine" id="cb14-15" title="15">  <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(<span class="st">"R package benchmark is not available"</span>)</a>
+<a class="sourceLine" id="cb14-16" title="16">}</a></code></pre></div>
 <pre><code>## Successfully compiled differential equation model from auto-generated C code.</code></pre>
+<pre><code>## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet =
+## TRUE): Observations with value of zero were removed from the data</code></pre>
+<pre><code>## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
+## value of zero were removed from the data</code></pre>
+<pre><code>## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet =
+## TRUE): Observations with value of zero were removed from the data
+
+## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet =
+## TRUE): Observations with value of zero were removed from the data
+
+## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet =
+## TRUE): Observations with value of zero were removed from the data</code></pre>
+<pre><code>## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
+## value of zero were removed from the data
+
+## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
+## value of zero were removed from the data
+
+## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
+## value of zero were removed from the data</code></pre>
 <pre><code>##                    test replications elapsed relative user.self sys.self
-## 2     deSolve, compiled            3   3.773    1.000     3.770        0
-## 1 deSolve, not compiled            3  27.812    7.371    27.798        0
+## 2     deSolve, compiled            3   4.783    1.000     4.780        0
+## 1 deSolve, not compiled            3  52.761   11.031    52.733        0
 ##   user.child sys.child
 ## 2          0         0
 ## 1          0         0</code></pre>
-<p>Here we get a performance benefit of a factor of 7 using the version of the differential equation model compiled from C code!</p>
-<p>This vignette was built with mkin 0.9.48.1 on</p>
+<p>Here we get a performance benefit of a factor of 11 using the version of the differential equation model compiled from C code!</p>
+<p>This vignette was built with mkin 0.9.49.6 on</p>
 <pre><code>## R version 3.6.0 (2019-04-26)
 ## Platform: x86_64-pc-linux-gnu (64-bit)
 ## Running under: Debian GNU/Linux 10 (buster)</code></pre>
author	Johannes Ranke <jranke@uni-bremen.de>	2019-07-08 18:12:21 +0200
committer	Johannes Ranke <jranke@uni-bremen.de>	2019-07-09 09:10:02 +0200
commit	e0bef15657df1d6cade99cc3f6d8b07fa35792fe (patch)
tree	7d050ac3b25e37a952a1f4efa46263980fbe502b /docs/articles
parent	67d032fb345f8e0afc7628d7525da5b7f0a98f79 (diff)