aboutsummaryrefslogtreecommitdiff
path: root/docs/articles/FOCUS_L.html
diff options
context:
space:
mode:
authorJohannes Ranke <jranke@uni-bremen.de>2022-05-18 21:26:17 +0200
committerJohannes Ranke <jranke@uni-bremen.de>2022-05-18 21:26:17 +0200
commit91c5db736a4d3f2290a0cc5698fb4e35ae7bda59 (patch)
tree8e9e34d18f055936172329c1248e6e2ff136bff9 /docs/articles/FOCUS_L.html
parentea57db98cef3fb882f7bd9656b44f270e7bded38 (diff)
Remove outdated comment in FOCUS L vignette, update docs
This also adds the first benchmark results obtained on my laptop system
Diffstat (limited to 'docs/articles/FOCUS_L.html')
-rw-r--r--docs/articles/FOCUS_L.html184
1 files changed, 88 insertions, 96 deletions
diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html
index d7412a56..5f41b6a3 100644
--- a/docs/articles/FOCUS_L.html
+++ b/docs/articles/FOCUS_L.html
@@ -105,7 +105,7 @@
<h1 data-toc-skip>Example evaluation of FOCUS Laboratory Data L1 to L3</h1>
<h4 data-toc-skip class="author">Johannes Ranke</h4>
- <h4 data-toc-skip class="date">Last change 17 November 2016 (rebuilt 2022-03-07)</h4>
+ <h4 data-toc-skip class="date">Last change 17 November 2016 (rebuilt 2022-05-18)</h4>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/FOCUS_L.rmd" class="external-link"><code>vignettes/FOCUS_L.rmd</code></a></small>
<div class="hidden name"><code>FOCUS_L.rmd</code></div>
@@ -132,16 +132,16 @@
<code class="sourceCode R"><span class="va">m.L1.SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L1_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L1.SFO</span><span class="op">)</span></code></pre></div>
<pre><code><span class="co">## mkin version used for fitting: 1.1.0 </span>
-<span class="co">## R version used for fitting: 4.1.2 </span>
-<span class="co">## Date of fit: Mon Mar 7 13:16:01 2022 </span>
-<span class="co">## Date of summary: Mon Mar 7 13:16:01 2022 </span>
+<span class="co">## R version used for fitting: 4.2.0 </span>
+<span class="co">## Date of fit: Wed May 18 20:42:32 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:32 2022 </span>
<span class="co">## </span>
<span class="co">## Equations:</span>
<span class="co">## d_parent/dt = - k_parent * parent</span>
<span class="co">## </span>
<span class="co">## Model predictions using solution type analytical </span>
<span class="co">## </span>
-<span class="co">## Fitted using 133 model solutions performed in 0.032 s</span>
+<span class="co">## Fitted using 133 model solutions performed in 0.031 s</span>
<span class="co">## </span>
<span class="co">## Error model: Constant variance </span>
<span class="co">## </span>
@@ -173,9 +173,9 @@
<span class="co">## </span>
<span class="co">## Parameter correlation:</span>
<span class="co">## parent_0 log_k_parent sigma</span>
-<span class="co">## parent_0 1.000e+00 6.186e-01 -1.516e-09</span>
-<span class="co">## log_k_parent 6.186e-01 1.000e+00 -3.124e-09</span>
-<span class="co">## sigma -1.516e-09 -3.124e-09 1.000e+00</span>
+<span class="co">## parent_0 1.000e+00 6.186e-01 -1.712e-09</span>
+<span class="co">## log_k_parent 6.186e-01 1.000e+00 -3.237e-09</span>
+<span class="co">## sigma -1.712e-09 -3.237e-09 1.000e+00</span>
<span class="co">## </span>
<span class="co">## Backtransformed parameters:</span>
<span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -225,29 +225,26 @@
<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="downlit sourceCode r">
-<code class="sourceCode R"><span class="va">m.L1.FOMC</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="va">FOCUS_2006_L1_mkin</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
-<pre><code><span class="co">## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:</span>
-<span class="co">## false convergence (8)</span></code></pre>
-<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">m.L1.FOMC</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>, main <span class="op">=</span> <span class="st">"FOCUS L1 - FOMC"</span><span class="op">)</span></code></pre></div>
+<code class="sourceCode R"><span class="va">m.L1.FOMC</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="va">FOCUS_2006_L1_mkin</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">m.L1.FOMC</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>, main <span class="op">=</span> <span class="st">"FOCUS L1 - FOMC"</span><span class="op">)</span></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="downlit sourceCode r">
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L1.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
<pre><code><span class="co">## Warning in sqrt(diag(covar)): NaNs produced</span></code></pre>
<pre><code><span class="co">## Warning in sqrt(1/diag(V)): NaNs produced</span></code></pre>
<pre><code><span class="co">## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is</span>
<span class="co">## doubtful</span></code></pre>
<pre><code><span class="co">## mkin version used for fitting: 1.1.0 </span>
-<span class="co">## R version used for fitting: 4.1.2 </span>
-<span class="co">## Date of fit: Mon Mar 7 13:16:02 2022 </span>
-<span class="co">## Date of summary: Mon Mar 7 13:16:02 2022 </span>
+<span class="co">## R version used for fitting: 4.2.0 </span>
+<span class="co">## Date of fit: Wed May 18 20:42:33 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:33 2022 </span>
<span class="co">## </span>
<span class="co">## Equations:</span>
<span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span>
<span class="co">## </span>
<span class="co">## Model predictions using solution type analytical </span>
<span class="co">## </span>
-<span class="co">## Fitted using 369 model solutions performed in 0.081 s</span>
+<span class="co">## Fitted using 357 model solutions performed in 0.072 s</span>
<span class="co">## </span>
<span class="co">## Error model: Constant variance </span>
<span class="co">## </span>
@@ -268,39 +265,34 @@
<span class="co">## Fixed parameter values:</span>
<span class="co">## None</span>
<span class="co">## </span>
-<span class="co">## </span>
-<span class="co">## Warning(s): </span>
-<span class="co">## Optimisation did not converge:</span>
-<span class="co">## false convergence (8)</span>
-<span class="co">## </span>
<span class="co">## Results:</span>
<span class="co">## </span>
-<span class="co">## AIC BIC logLik</span>
-<span class="co">## 95.88781 99.44929 -43.9439</span>
+<span class="co">## AIC BIC logLik</span>
+<span class="co">## 95.88804 99.44953 -43.94402</span>
<span class="co">## </span>
<span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span>
<span class="co">## Estimate Std. Error Lower Upper</span>
<span class="co">## parent_0 92.47 1.2820 89.720 95.220</span>
-<span class="co">## log_alpha 13.78 NaN NaN NaN</span>
-<span class="co">## log_beta 16.13 NaN NaN NaN</span>
-<span class="co">## sigma 2.78 0.4598 1.794 3.766</span>
+<span class="co">## log_alpha 11.37 NaN NaN NaN</span>
+<span class="co">## log_beta 13.72 NaN NaN NaN</span>
+<span class="co">## sigma 2.78 0.4621 1.789 3.771</span>
<span class="co">## </span>
<span class="co">## Parameter correlation:</span>
<span class="co">## parent_0 log_alpha log_beta sigma</span>
-<span class="co">## parent_0 1.0000000 NaN NaN 0.0001671</span>
+<span class="co">## parent_0 1.0000000 NaN NaN 0.0005548</span>
<span class="co">## log_alpha NaN 1 NaN NaN</span>
<span class="co">## log_beta NaN NaN 1 NaN</span>
-<span class="co">## sigma 0.0001671 NaN NaN 1.0000000</span>
+<span class="co">## sigma 0.0005548 NaN NaN 1.0000000</span>
<span class="co">## </span>
<span class="co">## Backtransformed parameters:</span>
<span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
<span class="co">## t-test (unrealistically) based on the assumption of normal distribution</span>
<span class="co">## for estimators of untransformed parameters.</span>
<span class="co">## Estimate t value Pr(&gt;t) Lower Upper</span>
-<span class="co">## parent_0 9.247e+01 NA NA 89.720 95.220</span>
-<span class="co">## alpha 9.658e+05 NA NA NA NA</span>
-<span class="co">## beta 1.010e+07 NA NA NA NA</span>
-<span class="co">## sigma 2.780e+00 NA NA 1.794 3.766</span>
+<span class="co">## parent_0 92.47 NA NA 89.720 95.220</span>
+<span class="co">## alpha 87110.00 NA NA NA NA</span>
+<span class="co">## beta 911100.00 NA NA NA NA</span>
+<span class="co">## sigma 2.78 NA NA 1.789 3.771</span>
<span class="co">## </span>
<span class="co">## FOCUS Chi2 error levels in percent:</span>
<span class="co">## err.min n.optim df</span>
@@ -308,8 +300,8 @@
<span class="co">## parent 3.619 3 6</span>
<span class="co">## </span>
<span class="co">## Estimated disappearance times:</span>
-<span class="co">## DT50 DT90 DT50back</span>
-<span class="co">## parent 7.25 24.08 7.25</span></code></pre>
+<span class="co">## DT50 DT90 DT50back</span>
+<span class="co">## parent 7.249 24.08 7.249</span></code></pre>
<p>We get a warning that the default optimisation algorithm <code>Port</code> did not converge, which is an indication that the model is overparameterised, <em>i.e.</em> contains too many parameters that are ill-defined as a consequence.</p>
<p>And in fact, due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the <span class="math inline">\(\chi^2\)</span> error level is actually higher for the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the parameters <code>log_alpha</code> and <code>log_beta</code> internally fitted in the model have excessive confidence intervals, that span more than 25 orders of magnitude (!) when backtransformed to the scale of <code>alpha</code> and <code>beta</code>. Also, the t-test for significant difference from zero does not indicate such a significant difference, with p-values greater than 0.1, and finally, the parameter correlation of <code>log_alpha</code> and <code>log_beta</code> is 1.000, clearly indicating that the model is overparameterised.</p>
<p>The <span class="math inline">\(\chi^2\)</span> error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same <span class="math inline">\(\chi^2\)</span> error levels as the kinfit package and the calculation routines of the kinfit package have been extensively compared to the results obtained by the KinGUI software, as documented in the kinfit package vignette. KinGUI was the first widely used standard package in this field. Also, the calculation of <span class="math inline">\(\chi^2\)</span> error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt <span class="citation">(Ranke 2014)</span>.</p>
@@ -318,7 +310,7 @@
<h2 id="laboratory-data-l2">Laboratory Data L2<a class="anchor" aria-label="anchor" href="#laboratory-data-l2"></a>
</h2>
<p>The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:</p>
-<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">FOCUS_2006_L2</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span>
t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">28</span><span class="op">)</span>, each <span class="op">=</span> <span class="fl">2</span><span class="op">)</span>,
parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</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>,
@@ -329,7 +321,7 @@
<h3 id="sfo-fit-for-l2">SFO fit for L2<a class="anchor" aria-label="anchor" href="#sfo-fit-for-l2"></a>
</h3>
<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="cb15"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">m.L2.SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L2_mkin</span>, quiet<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">m.L2.SFO</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>,
main <span class="op">=</span> <span class="st">"FOCUS L2 - SFO"</span><span class="op">)</span></code></pre></div>
@@ -342,24 +334,24 @@
<h3 id="fomc-fit-for-l2">FOMC fit for L2<a class="anchor" aria-label="anchor" href="#fomc-fit-for-l2"></a>
</h3>
<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="cb16"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">m.L2.FOMC</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="va">FOCUS_2006_L2_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">m.L2.FOMC</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>,
main <span class="op">=</span> <span class="st">"FOCUS L2 - FOMC"</span><span class="op">)</span></code></pre></div>
<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-9-1.png" width="672"></p>
-<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L2.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
<pre><code><span class="co">## mkin version used for fitting: 1.1.0 </span>
-<span class="co">## R version used for fitting: 4.1.2 </span>
-<span class="co">## Date of fit: Mon Mar 7 13:16:03 2022 </span>
-<span class="co">## Date of summary: Mon Mar 7 13:16:03 2022 </span>
+<span class="co">## R version used for fitting: 4.2.0 </span>
+<span class="co">## Date of fit: Wed May 18 20:42:33 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:33 2022 </span>
<span class="co">## </span>
<span class="co">## Equations:</span>
<span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span>
<span class="co">## </span>
<span class="co">## Model predictions using solution type analytical </span>
<span class="co">## </span>
-<span class="co">## Fitted using 239 model solutions performed in 0.049 s</span>
+<span class="co">## Fitted using 239 model solutions performed in 0.044 s</span>
<span class="co">## </span>
<span class="co">## Error model: Constant variance </span>
<span class="co">## </span>
@@ -394,10 +386,10 @@
<span class="co">## </span>
<span class="co">## Parameter correlation:</span>
<span class="co">## parent_0 log_alpha log_beta sigma</span>
-<span class="co">## parent_0 1.000e+00 -1.151e-01 -2.085e-01 -7.828e-09</span>
-<span class="co">## log_alpha -1.151e-01 1.000e+00 9.741e-01 -1.602e-07</span>
-<span class="co">## log_beta -2.085e-01 9.741e-01 1.000e+00 -1.372e-07</span>
-<span class="co">## sigma -7.828e-09 -1.602e-07 -1.372e-07 1.000e+00</span>
+<span class="co">## parent_0 1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09</span>
+<span class="co">## log_alpha -1.151e-01 1.000e+00 9.741e-01 -1.617e-07</span>
+<span class="co">## log_beta -2.085e-01 9.741e-01 1.000e+00 -1.387e-07</span>
+<span class="co">## sigma -7.637e-09 -1.617e-07 -1.387e-07 1.000e+00</span>
<span class="co">## </span>
<span class="co">## Backtransformed parameters:</span>
<span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -423,17 +415,17 @@
<h3 id="dfop-fit-for-l2">DFOP fit for L2<a class="anchor" aria-label="anchor" href="#dfop-fit-for-l2"></a>
</h3>
<p>Fitting the four parameter DFOP model further reduces the <span class="math inline">\(\chi^2\)</span> error level.</p>
-<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">m.L2.DFOP</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="va">FOCUS_2006_L2_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">m.L2.DFOP</span>, show_residuals <span class="op">=</span> <span class="cn">TRUE</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>,
main <span class="op">=</span> <span class="st">"FOCUS L2 - DFOP"</span><span class="op">)</span></code></pre></div>
<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-10-1.png" width="672"></p>
-<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">m.L2.DFOP</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
<pre><code><span class="co">## mkin version used for fitting: 1.1.0 </span>
-<span class="co">## R version used for fitting: 4.1.2 </span>
-<span class="co">## Date of fit: Mon Mar 7 13:16:03 2022 </span>
-<span class="co">## Date of summary: Mon Mar 7 13:16:03 2022 </span>
+<span class="co">## R version used for fitting: 4.2.0 </span>
+<span class="co">## Date of fit: Wed May 18 20:42:34 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:34 2022 </span>
<span class="co">## </span>
<span class="co">## Equations:</span>
<span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span>
@@ -442,7 +434,7 @@
<span class="co">## </span>
<span class="co">## Model predictions using solution type analytical </span>
<span class="co">## </span>
-<span class="co">## Fitted using 581 model solutions performed in 0.132 s</span>
+<span class="co">## Fitted using 581 model solutions performed in 0.121 s</span>
<span class="co">## </span>
<span class="co">## Error model: Constant variance </span>
<span class="co">## </span>
@@ -473,18 +465,18 @@
<span class="co">## Optimised, transformed parameters with symmetric confidence intervals:</span>
<span class="co">## Estimate Std. Error Lower Upper</span>
<span class="co">## parent_0 93.950 9.998e-01 91.5900 96.3100</span>
-<span class="co">## log_k1 3.112 1.842e+03 -4353.0000 4359.0000</span>
+<span class="co">## log_k1 3.113 1.845e+03 -4360.0000 4367.0000</span>
<span class="co">## log_k2 -1.088 6.285e-02 -1.2370 -0.9394</span>
<span class="co">## g_qlogis -0.399 9.946e-02 -0.6342 -0.1638</span>
<span class="co">## sigma 1.414 2.886e-01 0.7314 2.0960</span>
<span class="co">## </span>
<span class="co">## Parameter correlation:</span>
<span class="co">## parent_0 log_k1 log_k2 g_qlogis sigma</span>
-<span class="co">## parent_0 1.000e+00 6.783e-07 -3.390e-10 2.665e-01 -2.967e-10</span>
-<span class="co">## log_k1 6.783e-07 1.000e+00 1.116e-04 -2.196e-04 -1.031e-05</span>
-<span class="co">## log_k2 -3.390e-10 1.116e-04 1.000e+00 -7.903e-01 2.917e-09</span>
-<span class="co">## g_qlogis 2.665e-01 -2.196e-04 -7.903e-01 1.000e+00 -4.408e-09</span>
-<span class="co">## sigma -2.967e-10 -1.031e-05 2.917e-09 -4.408e-09 1.000e+00</span>
+<span class="co">## parent_0 1.000e+00 6.784e-07 -5.188e-10 2.665e-01 -5.800e-10</span>
+<span class="co">## log_k1 6.784e-07 1.000e+00 1.114e-04 -2.191e-04 -1.029e-05</span>
+<span class="co">## log_k2 -5.188e-10 1.114e-04 1.000e+00 -7.903e-01 5.080e-09</span>
+<span class="co">## g_qlogis 2.665e-01 -2.191e-04 -7.903e-01 1.000e+00 -7.991e-09</span>
+<span class="co">## sigma -5.800e-10 -1.029e-05 5.080e-09 -7.991e-09 1.000e+00</span>
<span class="co">## </span>
<span class="co">## Backtransformed parameters:</span>
<span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -492,7 +484,7 @@
<span class="co">## for estimators of untransformed parameters.</span>
<span class="co">## Estimate t value Pr(&gt;t) Lower Upper</span>
<span class="co">## parent_0 93.9500 9.397e+01 2.036e-12 91.5900 96.3100</span>
-<span class="co">## k1 22.4800 5.553e-04 4.998e-01 0.0000 Inf</span>
+<span class="co">## k1 22.4800 5.544e-04 4.998e-01 0.0000 Inf</span>
<span class="co">## k2 0.3369 1.591e+01 4.697e-07 0.2904 0.3909</span>
<span class="co">## g 0.4016 1.680e+01 3.238e-07 0.3466 0.4591</span>
<span class="co">## sigma 1.4140 4.899e+00 8.776e-04 0.7314 2.0960</span>
@@ -504,15 +496,15 @@
<span class="co">## </span>
<span class="co">## Estimated disappearance times:</span>
<span class="co">## DT50 DT90 DT50back DT50_k1 DT50_k2</span>
-<span class="co">## parent 0.5335 5.311 1.599 0.03084 2.058</span></code></pre>
-<p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion. However, the failure to calculate the covariance matrix indicates that the parameter estimates correlate excessively. Therefore, the FOMC model may be preferred for this dataset.</p>
+<span class="co">## parent 0.5335 5.311 1.599 0.03083 2.058</span></code></pre>
+<p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion.</p>
</div>
</div>
<div class="section level2">
<h2 id="laboratory-data-l3">Laboratory Data L3<a class="anchor" aria-label="anchor" href="#laboratory-data-l3"></a>
</h2>
<p>The following code defines example dataset L3 from the FOCUS kinetics report, p. 290.</p>
-<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">FOCUS_2006_L3</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span>
t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,
parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">97.8</span>, <span class="fl">60</span>, <span class="fl">51</span>, <span class="fl">43</span>, <span class="fl">35</span>, <span class="fl">22</span>, <span class="fl">15</span>, <span class="fl">12</span><span class="op">)</span><span class="op">)</span>
@@ -521,7 +513,7 @@
<h3 id="fit-multiple-models">Fit multiple models<a class="anchor" aria-label="anchor" href="#fit-multiple-models"></a>
</h3>
<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="cb23"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="co"># Only use one core here, not to offend the CRAN checks</span>
<span class="va">mm.L3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span><span class="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,
<span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="st">"FOCUS L3"</span> <span class="op">=</span> <span class="va">FOCUS_2006_L3_mkin</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
@@ -534,12 +526,12 @@
</h3>
<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="cb24"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code><span class="co">## mkin version used for fitting: 1.1.0 </span>
-<span class="co">## R version used for fitting: 4.1.2 </span>
-<span class="co">## Date of fit: Mon Mar 7 13:16:04 2022 </span>
-<span class="co">## Date of summary: Mon Mar 7 13:16:04 2022 </span>
+<span class="co">## R version used for fitting: 4.2.0 </span>
+<span class="co">## Date of fit: Wed May 18 20:42:34 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:35 2022 </span>
<span class="co">## </span>
<span class="co">## Equations:</span>
<span class="co">## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span>
@@ -548,7 +540,7 @@
<span class="co">## </span>
<span class="co">## Model predictions using solution type analytical </span>
<span class="co">## </span>
-<span class="co">## Fitted using 376 model solutions performed in 0.08 s</span>
+<span class="co">## Fitted using 376 model solutions performed in 0.073 s</span>
<span class="co">## </span>
<span class="co">## Error model: Constant variance </span>
<span class="co">## </span>
@@ -586,11 +578,11 @@
<span class="co">## </span>
<span class="co">## Parameter correlation:</span>
<span class="co">## parent_0 log_k1 log_k2 g_qlogis sigma</span>
-<span class="co">## parent_0 1.000e+00 1.732e-01 2.282e-02 4.009e-01 -9.664e-08</span>
-<span class="co">## log_k1 1.732e-01 1.000e+00 4.945e-01 -5.809e-01 7.147e-07</span>
-<span class="co">## log_k2 2.282e-02 4.945e-01 1.000e+00 -6.812e-01 1.022e-06</span>
-<span class="co">## g_qlogis 4.009e-01 -5.809e-01 -6.812e-01 1.000e+00 -7.926e-07</span>
-<span class="co">## sigma -9.664e-08 7.147e-07 1.022e-06 -7.926e-07 1.000e+00</span>
+<span class="co">## parent_0 1.000e+00 1.732e-01 2.282e-02 4.009e-01 -9.632e-08</span>
+<span class="co">## log_k1 1.732e-01 1.000e+00 4.945e-01 -5.809e-01 7.145e-07</span>
+<span class="co">## log_k2 2.282e-02 4.945e-01 1.000e+00 -6.812e-01 1.021e-06</span>
+<span class="co">## g_qlogis 4.009e-01 -5.809e-01 -6.812e-01 1.000e+00 -7.925e-07</span>
+<span class="co">## sigma -9.632e-08 7.145e-07 1.021e-06 -7.925e-07 1.000e+00</span>
<span class="co">## </span>
<span class="co">## Backtransformed parameters:</span>
<span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -622,7 +614,7 @@
<span class="co">## 60 parent 22.0 23.26 -1.25919</span>
<span class="co">## 91 parent 15.0 15.18 -0.18181</span>
<span class="co">## 120 parent 12.0 10.19 1.81395</span></code></pre>
-<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></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>
@@ -633,13 +625,13 @@
<h2 id="laboratory-data-l4">Laboratory Data L4<a class="anchor" aria-label="anchor" href="#laboratory-data-l4"></a>
</h2>
<p>The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:</p>
-<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">FOCUS_2006_L4</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span>
t <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">3</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">30</span>, <span class="fl">60</span>, <span class="fl">91</span>, <span class="fl">120</span><span class="op">)</span>,
parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</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><span class="op">)</span><span class="op">)</span>
<span class="va">FOCUS_2006_L4_mkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span><span class="op">(</span><span class="va">FOCUS_2006_L4</span><span class="op">)</span></code></pre></div>
<p>Fits of the SFO and FOMC models, plots and summaries are produced below:</p>
-<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="co"># Only use one core here, not to offend the CRAN checks</span>
<span class="va">mm.L4</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span><span class="op">)</span>, cores <span class="op">=</span> <span class="fl">1</span>,
<span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="st">"FOCUS L4"</span> <span class="op">=</span> <span class="va">FOCUS_2006_L4_mkin</span><span class="op">)</span>,
@@ -647,19 +639,19 @@
<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">)</span></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="cb29"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
<pre><code><span class="co">## mkin version used for fitting: 1.1.0 </span>
-<span class="co">## R version used for fitting: 4.1.2 </span>
-<span class="co">## Date of fit: Mon Mar 7 13:16:04 2022 </span>
-<span class="co">## Date of summary: Mon Mar 7 13:16:05 2022 </span>
+<span class="co">## R version used for fitting: 4.2.0 </span>
+<span class="co">## Date of fit: Wed May 18 20:42:35 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:35 2022 </span>
<span class="co">## </span>
<span class="co">## Equations:</span>
<span class="co">## d_parent/dt = - k_parent * parent</span>
<span class="co">## </span>
<span class="co">## Model predictions using solution type analytical </span>
<span class="co">## </span>
-<span class="co">## Fitted using 142 model solutions performed in 0.029 s</span>
+<span class="co">## Fitted using 142 model solutions performed in 0.027 s</span>
<span class="co">## </span>
<span class="co">## Error model: Constant variance </span>
<span class="co">## </span>
@@ -691,9 +683,9 @@
<span class="co">## </span>
<span class="co">## Parameter correlation:</span>
<span class="co">## parent_0 log_k_parent sigma</span>
-<span class="co">## parent_0 1.000e+00 5.938e-01 3.387e-07</span>
-<span class="co">## log_k_parent 5.938e-01 1.000e+00 5.830e-07</span>
-<span class="co">## sigma 3.387e-07 5.830e-07 1.000e+00</span>
+<span class="co">## parent_0 1.000e+00 5.938e-01 3.440e-07</span>
+<span class="co">## log_k_parent 5.938e-01 1.000e+00 5.885e-07</span>
+<span class="co">## sigma 3.440e-07 5.885e-07 1.000e+00</span>
<span class="co">## </span>
<span class="co">## Backtransformed parameters:</span>
<span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -712,19 +704,19 @@
<span class="co">## Estimated disappearance times:</span>
<span class="co">## DT50 DT90</span>
<span class="co">## parent 106 352</span></code></pre>
-<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
<pre><code><span class="co">## mkin version used for fitting: 1.1.0 </span>
-<span class="co">## R version used for fitting: 4.1.2 </span>
-<span class="co">## Date of fit: Mon Mar 7 13:16:04 2022 </span>
-<span class="co">## Date of summary: Mon Mar 7 13:16:05 2022 </span>
+<span class="co">## R version used for fitting: 4.2.0 </span>
+<span class="co">## Date of fit: Wed May 18 20:42:35 2022 </span>
+<span class="co">## Date of summary: Wed May 18 20:42:35 2022 </span>
<span class="co">## </span>
<span class="co">## Equations:</span>
<span class="co">## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span>
<span class="co">## </span>
<span class="co">## Model predictions using solution type analytical </span>
<span class="co">## </span>
-<span class="co">## Fitted using 224 model solutions performed in 0.045 s</span>
+<span class="co">## Fitted using 224 model solutions performed in 0.041 s</span>
<span class="co">## </span>
<span class="co">## Error model: Constant variance </span>
<span class="co">## </span>
@@ -759,10 +751,10 @@
<span class="co">## </span>
<span class="co">## Parameter correlation:</span>
<span class="co">## parent_0 log_alpha log_beta sigma</span>
-<span class="co">## parent_0 1.000e+00 -4.696e-01 -5.543e-01 -2.468e-07</span>
-<span class="co">## log_alpha -4.696e-01 1.000e+00 9.889e-01 2.478e-08</span>
-<span class="co">## log_beta -5.543e-01 9.889e-01 1.000e+00 5.211e-08</span>
-<span class="co">## sigma -2.468e-07 2.478e-08 5.211e-08 1.000e+00</span>
+<span class="co">## parent_0 1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07</span>
+<span class="co">## log_alpha -4.696e-01 1.000e+00 9.889e-01 4.066e-08</span>
+<span class="co">## log_beta -5.543e-01 9.889e-01 1.000e+00 6.818e-08</span>
+<span class="co">## sigma -2.563e-07 4.066e-08 6.818e-08 1.000e+00</span>
<span class="co">## </span>
<span class="co">## Backtransformed parameters:</span>
<span class="co">## Confidence intervals for internally transformed parameters are asymmetric.</span>
@@ -811,7 +803,7 @@
<div class="pkgdown">
<p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</p>
</div>
</footer>

Contact - Imprint