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<title>Example evaluation of FOCUS Laboratory Data L1 to L3</title>

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<h1 class="title toc-ignore">Example evaluation of FOCUS Laboratory Data
L1 to L3</h1>
<h4 class="author">Johannes Ranke</h4>
<h4 class="date">Last change 18 May 2023 (rebuilt 2025-02-16)</h4>


<div id="TOC">
<ul>
<li><a href="#laboratory-data-l1">Laboratory Data L1</a></li>
<li><a href="#laboratory-data-l2">Laboratory Data L2</a>
<ul>
<li><a href="#sfo-fit-for-l2">SFO fit for L2</a></li>
<li><a href="#fomc-fit-for-l2">FOMC fit for L2</a></li>
<li><a href="#dfop-fit-for-l2">DFOP fit for L2</a></li>
</ul></li>
<li><a href="#laboratory-data-l3">Laboratory Data L3</a>
<ul>
<li><a href="#fit-multiple-models">Fit multiple models</a></li>
<li><a href="#accessing-mmkin-objects">Accessing mmkin objects</a></li>
</ul></li>
<li><a href="#laboratory-data-l4">Laboratory Data L4</a></li>
<li><a href="#references">References</a></li>
</ul>
</div>

<div id="laboratory-data-l1" class="section level1">
<h1>Laboratory Data L1</h1>
<p>The following code defines example dataset L1 from the FOCUS kinetics
report, p. 284:</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(<span class="st">&quot;mkin&quot;</span>, <span class="at">quietly =</span> <span class="cn">TRUE</span>)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>FOCUS_2006_L1 <span class="ot">=</span> <span class="fu">data.frame</span>(</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">t =</span> <span class="fu">rep</span>(<span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>, <span class="dv">5</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">21</span>, <span class="dv">30</span>), <span class="at">each =</span> <span class="dv">2</span>),</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>  <span class="at">parent =</span> <span class="fu">c</span>(<span class="fl">88.3</span>, <span class="fl">91.4</span>, <span class="fl">85.6</span>, <span class="fl">84.5</span>, <span class="fl">78.9</span>, <span class="fl">77.6</span>,</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a>             <span class="fl">72.0</span>, <span class="fl">71.9</span>, <span class="fl">50.3</span>, <span class="fl">59.4</span>, <span class="fl">47.0</span>, <span class="fl">45.1</span>,</span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a>             <span class="fl">27.7</span>, <span class="fl">27.3</span>, <span class="fl">10.0</span>, <span class="fl">10.4</span>, <span class="fl">2.9</span>, <span class="fl">4.0</span>))</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a>FOCUS_2006_L1_mkin <span class="ot">&lt;-</span> <span class="fu">mkin_wide_to_long</span>(FOCUS_2006_L1)</span></code></pre></div>
<p>Here we use the assumptions of simple first order (SFO), the case of
declining rate constant over time (FOMC) and the case of two different
phases of the kinetics (DFOP). For a more detailed discussion of the
models, please see the FOCUS kinetics report.</p>
<p>Since mkin version 0.9-32 (July 2014), we can use shorthand notation
like <code>&quot;SFO&quot;</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"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>m.L1.SFO <span class="ot">&lt;-</span> <span class="fu">mkinfit</span>(<span class="st">&quot;SFO&quot;</span>, FOCUS_2006_L1_mkin, <span class="at">quiet =</span> <span class="cn">TRUE</span>)</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(m.L1.SFO)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<pre><code>## mkin version used for fitting:    0.9.49.8 
## R version used for fitting:       4.4.2 
## Date of fit:     Sun Feb 16 14:25:37 2025 
## Date of summary: Sun Feb 16 14:25:37 2025 
## 
## Equations:
## d_parent/dt = - k_parent_sink * parent
## 
## Model predictions using solution type analytical 
## 
## Fitted using 133 model solutions performed in 0.106 s
## 
## 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
## 
## 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
## 
## Fixed parameter values:
## None
## 
## Optimised, transformed parameters with symmetric confidence intervals:
##                   Estimate Std. Error  Lower  Upper
## 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      sigma
## parent_0           1.000e+00         6.186e-01 -1.516e-09
## log_k_parent_sink  6.186e-01         1.000e+00 -3.124e-09
## sigma             -1.516e-09        -3.124e-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   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
## 
## FOCUS Chi2 error levels in percent:
##          err.min n.optim df
## All data   3.424       2  7
## parent     3.424       2  7
## 
## Resulting formation fractions:
##             ff
## parent_sink  1
## 
## Estimated disappearance times:
##         DT50  DT90
## parent 7.249 24.08
## 
## Data:
##  time variable observed predicted residual
##     0   parent     88.3    92.471  -4.1710
##     0   parent     91.4    92.471  -1.0710
##     1   parent     85.6    84.039   1.5610
##     1   parent     84.5    84.039   0.4610
##     2   parent     78.9    76.376   2.5241
##     2   parent     77.6    76.376   1.2241
##     3   parent     72.0    69.412   2.5884
##     3   parent     71.9    69.412   2.4884
##     5   parent     50.3    57.330  -7.0301
##     5   parent     59.4    57.330   2.0699
##     7   parent     47.0    47.352  -0.3515
##     7   parent     45.1    47.352  -2.2515
##    14   parent     27.7    24.247   3.4528
##    14   parent     27.3    24.247   3.0528
##    21   parent     10.0    12.416  -2.4163
##    21   parent     10.4    12.416  -2.0163
##    30   parent      2.9     5.251  -2.3513
##    30   parent      4.0     5.251  -1.2513</code></pre>
<p>A plot of the fit is obtained with the plot function for mkinfit
objects.</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(m.L1.SFO, <span class="at">show_errmin =</span> <span class="cn">TRUE</span>, <span class="at">main =</span> <span class="st">&quot;FOCUS L1 - SFO&quot;</span>)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<p><img 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" /><!-- --></p>
<p>The residual plot can be easily obtained by</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="fu">mkinresplot</span>(m.L1.SFO, <span class="at">ylab =</span> <span class="st">&quot;Observed&quot;</span>, <span class="at">xlab =</span> <span class="st">&quot;Time&quot;</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>For comparison, the FOMC model is fitted as well, and the <span class="math inline"><em>χ</em><sup>2</sup></span> error level is
checked.</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>m.L1.FOMC <span class="ot">&lt;-</span> <span class="fu">mkinfit</span>(<span class="st">&quot;FOMC&quot;</span>, FOCUS_2006_L1_mkin, <span class="at">quiet=</span><span class="cn">TRUE</span>)</span></code></pre></div>
<pre><code>## Warning in mkinfit(&quot;FOMC&quot;, FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
## false convergence (8)</code></pre>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(m.L1.FOMC, <span class="at">show_errmin =</span> <span class="cn">TRUE</span>, <span class="at">main =</span> <span class="st">&quot;FOCUS L1 - FOMC&quot;</span>)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<p><img 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" /><!-- --></p>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(m.L1.FOMC, <span class="at">data =</span> <span class="cn">FALSE</span>)</span></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<pre><code>## Warning in cov2cor(ans$covar): diag(V) had non-positive or NA entries; the
## non-finite result may be dubious</code></pre>
<pre><code>## mkin version used for fitting:    0.9.49.8 
## R version used for fitting:       4.4.2 
## Date of fit:     Sun Feb 16 14:25:37 2025 
## Date of summary: Sun Feb 16 14:25:37 2025 
## 
## 
## Warning: Optimisation did not converge:
## false convergence (8) 
## 
## 
## Equations:
## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
## 
## Model predictions using solution type analytical 
## 
## Fitted using 342 model solutions performed in 0.242 s
## 
## 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
## 
## 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
## 
## Fixed parameter values:
## None
## 
## Optimised, transformed parameters with symmetric confidence intervals:
##           Estimate Std. Error  Lower  Upper
## parent_0     92.47     1.2820 89.720 95.220
## log_alpha    13.20        NaN    NaN    NaN
## log_beta     15.54        NaN    NaN    NaN
## sigma         2.78     0.4607  1.792  3.768
## 
## Parameter correlation:
##           parent_0 log_alpha log_beta    sigma
## parent_0  1.000000       NaN      NaN 0.000603
## log_alpha      NaN         1      NaN      NaN
## log_beta       NaN       NaN        1      NaN
## sigma     0.000603       NaN      NaN 1.000000
## 
## 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 9.247e+01      NA     NA 89.720 95.220
## alpha    5.386e+05      NA     NA     NA     NA
## beta     5.633e+06      NA     NA     NA     NA
## sigma    2.780e+00      NA     NA  1.792  3.768
## 
## FOCUS Chi2 error levels in percent:
##          err.min n.optim df
## All data   3.619       3  6
## parent     3.619       3  6
## 
## Estimated disappearance times:
##         DT50  DT90 DT50back
## parent 7.249 24.08    7.249</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"><em>χ</em><sup>2</sup></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"><em>χ</em><sup>2</sup></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"><em>χ</em><sup>2</sup></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"><em>χ</em><sup>2</sup></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>
</div>
<div id="laboratory-data-l2" class="section level1">
<h1>Laboratory Data L2</h1>
<p>The following code defines example dataset L2 from the FOCUS kinetics
report, p. 287:</p>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>FOCUS_2006_L2 <span class="ot">=</span> <span class="fu">data.frame</span>(</span>
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>  <span class="at">t =</span> <span class="fu">rep</span>(<span class="fu">c</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="at">each =</span> <span class="dv">2</span>),</span>
<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">parent =</span> <span class="fu">c</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>,</span>
<span id="cb17-4"><a href="#cb17-4" aria-hidden="true" tabindex="-1"></a>             <span class="fl">19.3</span>, <span class="fl">22.3</span>, <span class="fl">4.6</span>, <span class="fl">4.6</span>,</span>
<span id="cb17-5"><a href="#cb17-5" aria-hidden="true" tabindex="-1"></a>             <span class="fl">2.6</span>, <span class="fl">1.2</span>, <span class="fl">0.3</span>, <span class="fl">0.6</span>))</span>
<span id="cb17-6"><a href="#cb17-6" aria-hidden="true" tabindex="-1"></a>FOCUS_2006_L2_mkin <span class="ot">&lt;-</span> <span class="fu">mkin_wide_to_long</span>(FOCUS_2006_L2)</span></code></pre></div>
<div id="sfo-fit-for-l2" class="section level2">
<h2>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="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>m.L2.SFO <span class="ot">&lt;-</span> <span class="fu">mkinfit</span>(<span class="st">&quot;SFO&quot;</span>, FOCUS_2006_L2_mkin, <span class="at">quiet=</span><span class="cn">TRUE</span>)</span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(m.L2.SFO, <span class="at">show_residuals =</span> <span class="cn">TRUE</span>, <span class="at">show_errmin =</span> <span class="cn">TRUE</span>,</span>
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a>     <span class="at">main =</span> <span class="st">&quot;FOCUS L2 - SFO&quot;</span>)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<p><img 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/><!-- --></p>
<p>The <span class="math inline"><em>χ</em><sup>2</sup></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>
<p>We may add that it is difficult to judge the random nature of the
residuals just from the three samplings at days 0, 1 and 3. Also, it is
not clear <em>a priori</em> why a consistent underestimation after the
approximate DT90 should be irrelevant. However, this can be rationalised
by the fact that the FOCUS fate models generally only implement SFO
kinetics.</p>
</div>
<div id="fomc-fit-for-l2" class="section level2">
<h2>FOMC fit for L2</h2>
<p>For comparison, the FOMC model is fitted as well, and the <span class="math inline"><em>χ</em><sup>2</sup></span> error level is
checked.</p>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>m.L2.FOMC <span class="ot">&lt;-</span> <span class="fu">mkinfit</span>(<span class="st">&quot;FOMC&quot;</span>, FOCUS_2006_L2_mkin, <span class="at">quiet =</span> <span class="cn">TRUE</span>)</span>
<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(m.L2.FOMC, <span class="at">show_residuals =</span> <span class="cn">TRUE</span>,</span>
<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a>     <span class="at">main =</span> <span class="st">&quot;FOCUS L2 - FOMC&quot;</span>)</span></code></pre></div>
<p><img 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/><!-- --></p>
<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(m.L2.FOMC, <span class="at">data =</span> <span class="cn">FALSE</span>)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<pre><code>## mkin version used for fitting:    0.9.49.8 
## R version used for fitting:       4.4.2 
## Date of fit:     Sun Feb 16 14:25:38 2025 
## Date of summary: Sun Feb 16 14:25:38 2025 
## 
## Equations:
## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
## 
## Model predictions using solution type analytical 
## 
## Fitted using 239 model solutions performed in 0.167 s
## 
## Error model: Constant variance 
## 
## 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
## 
## 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
## 
## Fixed parameter values:
## None
## 
## Optimised, transformed parameters with symmetric confidence intervals:
##           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      sigma
## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.436e-09
## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07
## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.386e-07
## sigma     -7.436e-09 -1.617e-07 -1.386e-07  1.000e+00
## 
## 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  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
## 
## FOCUS Chi2 error levels in percent:
##          err.min n.optim df
## All data   6.205       3  3
## parent     6.205       3  3
## 
## Estimated disappearance times:
##          DT50  DT90 DT50back
## parent 0.8092 5.356    1.612</code></pre>
<p>The error level at which the <span class="math inline"><em>χ</em><sup>2</sup></span> test passes is much
lower in this case. Therefore, the FOMC model provides a better
description of the data, as less experimental error has to be assumed in
order to explain the data.</p>
</div>
<div id="dfop-fit-for-l2" class="section level2">
<h2>DFOP fit for L2</h2>
<p>Fitting the four parameter DFOP model further reduces the <span class="math inline"><em>χ</em><sup>2</sup></span> error level.</p>
<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a>m.L2.DFOP <span class="ot">&lt;-</span> <span class="fu">mkinfit</span>(<span class="st">&quot;DFOP&quot;</span>, FOCUS_2006_L2_mkin, <span class="at">quiet =</span> <span class="cn">TRUE</span>)</span>
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(m.L2.DFOP, <span class="at">show_residuals =</span> <span class="cn">TRUE</span>, <span class="at">show_errmin =</span> <span class="cn">TRUE</span>,</span>
<span id="cb24-3"><a href="#cb24-3" aria-hidden="true" tabindex="-1"></a>     <span class="at">main =</span> <span class="st">&quot;FOCUS L2 - DFOP&quot;</span>)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<p><img 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/><!-- --></p>
<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(m.L2.DFOP, <span class="at">data =</span> <span class="cn">FALSE</span>)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<pre><code>## mkin version used for fitting:    0.9.49.8 
## R version used for fitting:       4.4.2 
## Date of fit:     Sun Feb 16 14:25:39 2025 
## Date of summary: Sun Feb 16 14:25:39 2025 
## 
## Equations:
## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
##            * parent
## 
## Model predictions using solution type analytical 
## 
## Fitted using 572 model solutions performed in 0.399 s
## 
## 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
## 
## Starting values for the transformed parameters actually optimised:
##              value lower upper
## parent_0 93.950000  -Inf   Inf
## log_k1   -2.302585  -Inf   Inf
## log_k2   -4.605170  -Inf   Inf
## g_ilr     0.000000  -Inf   Inf
## 
## Fixed parameter values:
## None
## 
## Optimised, transformed parameters with symmetric confidence intervals:
##          Estimate Std. Error      Lower     Upper
## parent_0  93.9500  9.998e-01    91.5900   96.3100
## log_k1     3.1370  2.376e+03 -5615.0000 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:
##            parent_0     log_k1     log_k2      g_ilr      sigma
## parent_0  1.000e+00  5.144e-07  2.339e-09  2.665e-01 -6.798e-09
## log_k1    5.144e-07  1.000e+00  8.434e-05 -1.659e-04 -7.791e-06
## log_k2    2.339e-09  8.434e-05  1.000e+00 -7.903e-01 -1.240e-08
## g_ilr     2.665e-01 -1.659e-04 -7.903e-01  1.000e+00  3.195e-08
## sigma    -6.798e-09 -7.791e-06 -1.240e-08  3.195e-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 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
## 
## Estimated disappearance times:
##          DT50  DT90 DT50_k1 DT50_k2
## parent 0.5335 5.311 0.03009   2.058</code></pre>
<p>Here, the DFOP model is clearly the best-fit model for dataset L2
based on the chi^2 error level criterion.</p>
</div>
</div>
<div id="laboratory-data-l3" class="section level1">
<h1>Laboratory Data L3</h1>
<p>The following code defines example dataset L3 from the FOCUS kinetics
report, p. 290.</p>
<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a>FOCUS_2006_L3 <span class="ot">=</span> <span class="fu">data.frame</span>(</span>
<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a>  <span class="at">t =</span> <span class="fu">c</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>),</span>
<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">parent =</span> <span class="fu">c</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>))</span>
<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a>FOCUS_2006_L3_mkin <span class="ot">&lt;-</span> <span class="fu">mkin_wide_to_long</span>(FOCUS_2006_L3)</span></code></pre></div>
<div id="fit-multiple-models" class="section level2">
<h2>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="cb30"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Only use one core here, not to offend the CRAN checks</span></span>
<span id="cb30-2"><a href="#cb30-2" aria-hidden="true" tabindex="-1"></a>mm.L3 <span class="ot">&lt;-</span> <span class="fu">mmkin</span>(<span class="fu">c</span>(<span class="st">&quot;SFO&quot;</span>, <span class="st">&quot;FOMC&quot;</span>, <span class="st">&quot;DFOP&quot;</span>), <span class="at">cores =</span> <span class="dv">1</span>,</span>
<span id="cb30-3"><a href="#cb30-3" aria-hidden="true" tabindex="-1"></a>               <span class="fu">list</span>(<span class="st">&quot;FOCUS L3&quot;</span> <span class="ot">=</span> FOCUS_2006_L3_mkin), <span class="at">quiet =</span> <span class="cn">TRUE</span>)</span>
<span id="cb30-4"><a href="#cb30-4" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(mm.L3)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded
## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded
## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>The <span class="math inline"><em>χ</em><sup>2</sup></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"><em>χ</em><sup>2</sup></span> test passes
of 7%. Fitting the four parameter DFOP model further reduces the <span class="math inline"><em>χ</em><sup>2</sup></span> error level
considerably.</p>
</div>
<div id="accessing-mmkin-objects" class="section level2">
<h2>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="cb32"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(mm.L3[[<span class="st">&quot;DFOP&quot;</span>, <span class="dv">1</span>]])</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<pre><code>## mkin version used for fitting:    0.9.49.8 
## R version used for fitting:       4.4.2 
## Date of fit:     Sun Feb 16 14:25:40 2025 
## Date of summary: Sun Feb 16 14:25:40 2025 
## 
## Equations:
## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
##            * parent
## 
## Model predictions using solution type analytical 
## 
## Fitted using 373 model solutions performed in 0.258 s
## 
## 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
## 
## Starting values for the transformed parameters actually optimised:
##              value lower upper
## parent_0 97.800000  -Inf   Inf
## log_k1   -2.302585  -Inf   Inf
## log_k2   -4.605170  -Inf   Inf
## g_ilr     0.000000  -Inf   Inf
## 
## Fixed parameter values:
## None
## 
## Optimised, transformed parameters with symmetric confidence intervals:
##          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      sigma
## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -6.814e-07
## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  3.193e-07
## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  7.661e-07
## g_ilr     4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -8.680e-07
## sigma    -6.814e-07  3.193e-07  7.661e-07 -8.680e-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  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
## 
## FOCUS Chi2 error levels in percent:
##          err.min n.optim df
## All data   2.225       4  4
## parent     2.225       4  4
## 
## Estimated disappearance times:
##         DT50 DT90 DT50_k1 DT50_k2
## parent 7.464  123   1.343   50.37
## 
## Data:
##  time variable observed predicted residual
##     0   parent     97.8     97.75  0.05396
##     3   parent     60.0     60.45 -0.44933
##     7   parent     51.0     49.44  1.56338
##    14   parent     43.0     43.84 -0.83632
##    30   parent     35.0     35.15 -0.14707
##    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="cb35"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb35-1"><a href="#cb35-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(mm.L3[[<span class="st">&quot;DFOP&quot;</span>, <span class="dv">1</span>]], <span class="at">show_errmin =</span> <span class="cn">TRUE</span>)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<p><img src="data:image/png;base64,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" /><!-- --></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"><em>χ</em><sup>2</sup></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>
</div>
</div>
<div id="laboratory-data-l4" class="section level1">
<h1>Laboratory Data L4</h1>
<p>The following code defines example dataset L4 from the FOCUS kinetics
report, p. 293:</p>
<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb37-1"><a href="#cb37-1" aria-hidden="true" tabindex="-1"></a>FOCUS_2006_L4 <span class="ot">=</span> <span class="fu">data.frame</span>(</span>
<span id="cb37-2"><a href="#cb37-2" aria-hidden="true" tabindex="-1"></a>  <span class="at">t =</span> <span class="fu">c</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>),</span>
<span id="cb37-3"><a href="#cb37-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">parent =</span> <span class="fu">c</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>
<span id="cb37-4"><a href="#cb37-4" aria-hidden="true" tabindex="-1"></a>FOCUS_2006_L4_mkin <span class="ot">&lt;-</span> <span class="fu">mkin_wide_to_long</span>(FOCUS_2006_L4)</span></code></pre></div>
<p>Fits of the SFO and FOMC models, plots and summaries are produced
below:</p>
<div class="sourceCode" id="cb38"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb38-1"><a href="#cb38-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Only use one core here, not to offend the CRAN checks</span></span>
<span id="cb38-2"><a href="#cb38-2" aria-hidden="true" tabindex="-1"></a>mm.L4 <span class="ot">&lt;-</span> <span class="fu">mmkin</span>(<span class="fu">c</span>(<span class="st">&quot;SFO&quot;</span>, <span class="st">&quot;FOMC&quot;</span>), <span class="at">cores =</span> <span class="dv">1</span>,</span>
<span id="cb38-3"><a href="#cb38-3" aria-hidden="true" tabindex="-1"></a>               <span class="fu">list</span>(<span class="st">&quot;FOCUS L4&quot;</span> <span class="ot">=</span> FOCUS_2006_L4_mkin),</span>
<span id="cb38-4"><a href="#cb38-4" aria-hidden="true" tabindex="-1"></a>               <span class="at">quiet =</span> <span class="cn">TRUE</span>)</span>
<span id="cb38-5"><a href="#cb38-5" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(mm.L4)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded
## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<p><img 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" /><!-- --></p>
<p>The <span class="math inline"><em>χ</em><sup>2</sup></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"><em>χ</em><sup>2</sup></span> test passes is
slightly lower for the FOMC model. However, the difference appears
negligible.</p>
<div class="sourceCode" id="cb40"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb40-1"><a href="#cb40-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(mm.L4[[<span class="st">&quot;SFO&quot;</span>, <span class="dv">1</span>]], <span class="at">data =</span> <span class="cn">FALSE</span>)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<pre><code>## mkin version used for fitting:    0.9.49.8 
## R version used for fitting:       4.4.2 
## Date of fit:     Sun Feb 16 14:25:40 2025 
## Date of summary: Sun Feb 16 14:25:40 2025 
## 
## Equations:
## d_parent/dt = - k_parent_sink * parent
## 
## Model predictions using solution type analytical 
## 
## Fitted using 142 model solutions performed in 0.096 s
## 
## 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
## 
## 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
## 
## Fixed parameter values:
## None
## 
## Optimised, transformed parameters with symmetric confidence intervals:
##                   Estimate Std. Error  Lower   Upper
## 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     sigma
## parent_0          1.000e+00         5.938e-01 3.430e-07
## log_k_parent_sink 5.938e-01         1.000e+00 5.885e-07
## sigma             3.430e-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   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
## 
## FOCUS Chi2 error levels in percent:
##          err.min n.optim df
## All data   3.287       2  6
## parent     3.287       2  6
## 
## Resulting formation fractions:
##             ff
## parent_sink  1
## 
## Estimated disappearance times:
##        DT50 DT90
## parent  106  352</code></pre>
<div class="sourceCode" id="cb43"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb43-1"><a href="#cb43-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(mm.L4[[<span class="st">&quot;FOMC&quot;</span>, <span class="dv">1</span>]], <span class="at">data =</span> <span class="cn">FALSE</span>)</span></code></pre></div>
<pre><code>## Warning: In subset.data.frame(fit$fixed, type = &quot;state&quot;) :
##  extra argument &#39;type&#39; will be disregarded</code></pre>
<pre><code>## mkin version used for fitting:    0.9.49.8 
## R version used for fitting:       4.4.2 
## Date of fit:     Sun Feb 16 14:25:40 2025 
## Date of summary: Sun Feb 16 14:25:40 2025 
## 
## Equations:
## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
## 
## Model predictions using solution type analytical 
## 
## Fitted using 224 model solutions performed in 0.151 s
## 
## 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
## 
## 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
## 
## Fixed parameter values:
## None
## 
## Optimised, transformed parameters with symmetric confidence intervals:
##           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      sigma
## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.447e-07
## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.198e-08
## log_beta  -5.543e-01  9.889e-01  1.000e+00  4.923e-08
## sigma     -2.447e-07  2.198e-08  4.923e-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  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
## 
## FOCUS Chi2 error levels in percent:
##          err.min n.optim df
## All data   2.029       3  5
## parent     2.029       3  5
## 
## Estimated disappearance times:
##         DT50 DT90 DT50back
## parent 108.9 1644    494.9</code></pre>
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<div id="references" class="section level1 unnumbered">
<h1 class="unnumbered">References</h1>
<div id="refs" class="references csl-bib-body hanging-indent">
<div id="ref-ranke2014" class="csl-entry">
Ranke, Johannes. 2014. <span>“<span class="nocase">Prüfung und
Validierung von Modellierungssoftware als Alternative zu ModelMaker
4.0</span>.”</span> Umweltbundesamt Projektnummer 27452.
</div>
</div>
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