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@@ -32,7 +32,7 @@
</button>
<span class="navbar-brand">
<a class="navbar-link" href="../index.html">mkin</a>
- <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.3</span>
+ <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span>
</span>
</div>
@@ -80,7 +80,7 @@
</ul>
<ul class="nav navbar-nav navbar-right">
<li>
- <a href="http://github.com/jranke/mkin/">
+ <a href="https://github.com/jranke/mkin/">
<span class="fab fa fab fa-github fa-lg"></span>
</a>
@@ -95,15 +95,16 @@
- </header><div class="row">
+ </header><link href="FOCUS_L_files/anchor-sections-1.0/anchor-sections.css" rel="stylesheet">
+<script src="FOCUS_L_files/anchor-sections-1.0/anchor-sections.js"></script><div class="row">
<div class="col-md-9 contents">
<div class="page-header toc-ignore">
<h1 data-toc-skip>Example evaluation of FOCUS Laboratory Data L1 to L3</h1>
<h4 class="author">Johannes Ranke</h4>
- <h4 class="date">2020-10-08</h4>
+ <h4 class="date">2020-11-19</h4>
- <small class="dont-index">Source: <a href="http://github.com/jranke/mkin/blob/master/vignettes/FOCUS_L.rmd"><code>vignettes/FOCUS_L.rmd</code></a></small>
+ <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/FOCUS_L.rmd"><code>vignettes/FOCUS_L.rmd</code></a></small>
<div class="hidden name"><code>FOCUS_L.rmd</code></div>
</div>
@@ -114,28 +115,30 @@
<h1 class="hasAnchor">
<a href="#laboratory-data-l1" class="anchor"></a>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"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/library.html">library</a></span>(<span class="st">"mkin"</span>, <span class="kw">quietly</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="no">FOCUS_2006_L1</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span>(
- <span class="kw">t</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">5</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">21</span>, <span class="fl">30</span>), <span class="kw">each</span> <span class="kw">=</span> <span class="fl">2</span>),
- <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></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>,
+<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="va">FOCUS_2006_L1</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">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">rep</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span>, <span class="fl">5</span>, <span class="fl">7</span>, <span class="fl">14</span>, <span class="fl">21</span>, <span class="fl">30</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">c</a></span><span class="op">(</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 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 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 class="no">FOCUS_2006_L1_mkin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(<span class="no">FOCUS_2006_L1</span>)</pre></body></html></div>
+ <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 class="op">)</span><span class="op">)</span>
+<span class="va">FOCUS_2006_L1_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_L1</span><span class="op">)</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>"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"><html><body><pre class="r"><span class="no">m.L1.SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"SFO"</span>, <span class="no">FOCUS_2006_L1_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L1.SFO</span>)</pre></body></html></div>
-<pre><code>## mkin version used for fitting: 0.9.50.3
-## R version used for fitting: 4.0.2
-## Date of fit: Thu Oct 8 09:14:05 2020
-## Date of summary: Thu Oct 8 09:14:05 2020
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="va">m.L1.SFO</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">FOCUS_2006_L1_mkin</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>
+<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">m.L1.SFO</span><span class="op">)</span></code></pre></div>
+<pre><code>## mkin version used for fitting: 0.9.50.4
+## R version used for fitting: 4.0.3
+## Date of fit: Thu Nov 19 15:00:09 2020
+## Date of summary: Thu Nov 19 15:00:09 2020
##
## Equations:
## d_parent/dt = - k_parent * parent
##
## Model predictions using solution type analytical
##
-## Fitted using 133 model solutions performed in 0.032 s
+## Fitted using 133 model solutions performed in 0.034 s
##
## Error model: Constant variance
##
@@ -210,33 +213,38 @@
## 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="cb4"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">m.L1.SFO</span>, <span class="kw">show_errmin</span> <span class="kw">=</span> <span class="fl">TRUE</span>, <span class="kw">main</span> <span class="kw">=</span> <span class="st">"FOCUS L1 - SFO"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">m.L1.SFO</span>, show_errmin <span class="op">=</span> <span class="cn">TRUE</span>, main <span class="op">=</span> <span class="st">"FOCUS L1 - SFO"</span><span class="op">)</span></code></pre></div>
<p><img src="FOCUS_L_files/figure-html/unnamed-chunk-4-1.png" width="576"></p>
<p>The residual plot can be easily obtained by</p>
-<div class="sourceCode" id="cb5"><html><body><pre class="r"><span class="fu"><a href="../reference/mkinresplot.html">mkinresplot</a></span>(<span class="no">m.L1.SFO</span>, <span class="kw">ylab</span> <span class="kw">=</span> <span class="st">"Observed"</span>, <span class="kw">xlab</span> <span class="kw">=</span> <span class="st">"Time"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="../reference/mkinresplot.html">mkinresplot</a></span><span class="op">(</span><span class="va">m.L1.SFO</span>, ylab <span class="op">=</span> <span class="st">"Observed"</span>, xlab <span class="op">=</span> <span class="st">"Time"</span><span class="op">)</span></code></pre></div>
<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"><html><body><pre class="r"><span class="no">m.L1.FOMC</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"FOMC"</span>, <span class="no">FOCUS_2006_L1_mkin</span>, <span class="kw">quiet</span><span class="kw">=</span><span class="fl">TRUE</span>)</pre></body></html></div>
+<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>## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
## false convergence (8)</code></pre>
-<div class="sourceCode" id="cb8"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">m.L1.FOMC</span>, <span class="kw">show_errmin</span> <span class="kw">=</span> <span class="fl">TRUE</span>, <span class="kw">main</span> <span class="kw">=</span> <span class="st">"FOCUS L1 - FOMC"</span>)</pre></body></html></div>
+<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-method.html">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"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L1.FOMC</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">m.L1.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
## doubtful</code></pre>
-<pre><code>## mkin version used for fitting: 0.9.50.3
-## R version used for fitting: 4.0.2
-## Date of fit: Thu Oct 8 09:14:05 2020
-## Date of summary: Thu Oct 8 09:14:05 2020
+<pre><code>## mkin version used for fitting: 0.9.50.4
+## R version used for fitting: 4.0.3
+## Date of fit: Thu Nov 19 15:00:09 2020
+## Date of summary: Thu Nov 19 15:00:09 2020
##
## Equations:
## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
##
## Model predictions using solution type analytical
##
-## Fitted using 380 model solutions performed in 0.088 s
+## Fitted using 380 model solutions performed in 0.085 s
##
## Error model: Constant variance
##
@@ -307,19 +315,21 @@
<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="cb14"><html><body><pre class="r"><span class="no">FOCUS_2006_L2</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span>(
- <span class="kw">t</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></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="kw">each</span> <span class="kw">=</span> <span class="fl">2</span>),
- <span class="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">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>,
+<div class="sourceCode" id="cb14"><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">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">rep</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="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">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>,
<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 class="fl">2.6</span>, <span class="fl">1.2</span>, <span class="fl">0.3</span>, <span class="fl">0.6</span>))
-<span class="no">FOCUS_2006_L2_mkin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(<span class="no">FOCUS_2006_L2</span>)</pre></body></html></div>
+ <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 class="op">)</span><span class="op">)</span>
+<span class="va">FOCUS_2006_L2_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_L2</span><span class="op">)</span></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="cb15"><html><body><pre class="r"><span class="no">m.L2.SFO</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"SFO"</span>, <span class="no">FOCUS_2006_L2_mkin</span>, <span class="kw">quiet</span><span class="kw">=</span><span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">m.L2.SFO</span>, <span class="kw">show_residuals</span> <span class="kw">=</span> <span class="fl">TRUE</span>, <span class="kw">show_errmin</span> <span class="kw">=</span> <span class="fl">TRUE</span>,
- <span class="kw">main</span> <span class="kw">=</span> <span class="st">"FOCUS L2 - SFO"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb15"><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-method.html">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>
<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>
@@ -329,22 +339,24 @@
<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="cb16"><html><body><pre class="r"><span class="no">m.L2.FOMC</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"FOMC"</span>, <span class="no">FOCUS_2006_L2_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">m.L2.FOMC</span>, <span class="kw">show_residuals</span> <span class="kw">=</span> <span class="fl">TRUE</span>,
- <span class="kw">main</span> <span class="kw">=</span> <span class="st">"FOCUS L2 - FOMC"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb16"><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-method.html">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"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L2.FOMC</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
-<pre><code>## mkin version used for fitting: 0.9.50.3
-## R version used for fitting: 4.0.2
-## Date of fit: Thu Oct 8 09:14:06 2020
-## Date of summary: Thu Oct 8 09:14:06 2020
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">m.L2.FOMC</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
+<pre><code>## mkin version used for fitting: 0.9.50.4
+## R version used for fitting: 4.0.3
+## Date of fit: Thu Nov 19 15:00:10 2020
+## Date of summary: Thu Nov 19 15:00:10 2020
##
## Equations:
## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
##
## Model predictions using solution type analytical
##
-## Fitted using 239 model solutions performed in 0.049 s
+## Fitted using 239 model solutions performed in 0.051 s
##
## Error model: Constant variance
##
@@ -408,15 +420,17 @@
<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="cb19"><html><body><pre class="r"><span class="no">m.L2.DFOP</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"DFOP"</span>, <span class="no">FOCUS_2006_L2_mkin</span>, <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">m.L2.DFOP</span>, <span class="kw">show_residuals</span> <span class="kw">=</span> <span class="fl">TRUE</span>, <span class="kw">show_errmin</span> <span class="kw">=</span> <span class="fl">TRUE</span>,
- <span class="kw">main</span> <span class="kw">=</span> <span class="st">"FOCUS L2 - DFOP"</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb19"><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-method.html">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"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">m.L2.DFOP</span>, <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
-<pre><code>## mkin version used for fitting: 0.9.50.3
-## R version used for fitting: 4.0.2
-## Date of fit: Thu Oct 8 09:14:06 2020
-## Date of summary: Thu Oct 8 09:14:06 2020
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">m.L2.DFOP</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
+<pre><code>## mkin version used for fitting: 0.9.50.4
+## R version used for fitting: 4.0.3
+## Date of fit: Thu Nov 19 15:00:10 2020
+## Date of summary: Thu Nov 19 15:00:10 2020
##
## Equations:
## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -425,7 +439,7 @@
##
## Model predictions using solution type analytical
##
-## Fitted using 572 model solutions performed in 0.136 s
+## Fitted using 581 model solutions performed in 0.138 s
##
## Error model: Constant variance
##
@@ -443,7 +457,7 @@
## parent_0 93.950000 -Inf Inf
## log_k1 -2.302585 -Inf Inf
## log_k2 -4.605170 -Inf Inf
-## g_ilr 0.000000 -Inf Inf
+## g_qlogis 0.000000 -Inf Inf
##
## Fixed parameter values:
## None
@@ -455,19 +469,19 @@
##
## 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
+## parent_0 93.950 9.998e-01 91.5900 96.3100
+## log_k1 3.117 1.929e+03 -4558.0000 4564.0000
+## log_k2 -1.088 6.285e-02 -1.2370 -0.9394
+## g_qlogis -0.399 9.946e-02 -0.6342 -0.1638
+## sigma 1.414 2.886e-01 0.7314 2.0960
##
## Parameter correlation:
-## parent_0 log_k1 log_k2 g_ilr sigma
-## parent_0 1.000e+00 5.157e-07 2.376e-09 2.665e-01 -6.837e-09
-## log_k1 5.157e-07 1.000e+00 8.434e-05 -1.659e-04 -7.786e-06
-## log_k2 2.376e-09 8.434e-05 1.000e+00 -7.903e-01 -1.263e-08
-## g_ilr 2.665e-01 -1.659e-04 -7.903e-01 1.000e+00 3.248e-08
-## sigma -6.837e-09 -7.786e-06 -1.263e-08 3.248e-08 1.000e+00
+## parent_0 log_k1 log_k2 g_qlogis sigma
+## parent_0 1.000e+00 6.459e-07 9.147e-11 2.665e-01 8.413e-11
+## log_k1 6.459e-07 1.000e+00 1.061e-04 -2.087e-04 -9.802e-06
+## log_k2 9.147e-11 1.061e-04 1.000e+00 -7.903e-01 -2.429e-09
+## g_qlogis 2.665e-01 -2.087e-04 -7.903e-01 1.000e+00 4.049e-09
+## sigma 8.413e-11 -9.802e-06 -2.429e-09 4.049e-09 1.000e+00
##
## Backtransformed parameters:
## Confidence intervals for internally transformed parameters are asymmetric.
@@ -475,7 +489,7 @@
## for estimators of untransformed parameters.
## Estimate t value Pr(&gt;t) Lower Upper
## parent_0 93.9500 9.397e+01 2.036e-12 91.5900 96.3100
-## k1 23.0400 4.303e-04 4.998e-01 0.0000 Inf
+## k1 22.5800 5.303e-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
@@ -487,7 +501,7 @@
##
## Estimated disappearance times:
## DT50 DT90 DT50back DT50_k1 DT50_k2
-## parent 0.5335 5.311 1.599 0.03009 2.058</code></pre>
+## parent 0.5335 5.311 1.599 0.0307 2.058</code></pre>
<p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion. However, the failure to calculate the covariance matrix indicates that the parameter estimates correlate excessively. Therefore, the FOMC model may be preferred for this dataset.</p>
</div>
</div>
@@ -495,18 +509,20 @@
<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="cb22"><html><body><pre class="r"><span class="no">FOCUS_2006_L3</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span>(
- <span class="kw">t</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></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="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></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="no">FOCUS_2006_L3_mkin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(<span class="no">FOCUS_2006_L3</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb22"><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">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">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">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>
+<span class="va">FOCUS_2006_L3_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_L3</span><span class="op">)</span></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="cb23"><html><body><pre class="r"><span class="co"># Only use one core here, not to offend the CRAN checks</span>
-<span class="no">mm.L3</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>), <span class="kw">cores</span> <span class="kw">=</span> <span class="fl">1</span>,
- <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="st">"FOCUS L3"</span> <span class="kw">=</span> <span class="no">FOCUS_2006_L3_mkin</span>), <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">mm.L3</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb23"><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">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">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>
+<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">)</span></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>
@@ -515,11 +531,12 @@
<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="cb24"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">mm.L3</span><span class="kw">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span>]])</pre></body></html></div>
-<pre><code>## mkin version used for fitting: 0.9.50.3
-## R version used for fitting: 4.0.2
-## Date of fit: Thu Oct 8 09:14:07 2020
-## Date of summary: Thu Oct 8 09:14:07 2020
+<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">mm.L3</span><span class="op">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
+<pre><code>## mkin version used for fitting: 0.9.50.4
+## R version used for fitting: 4.0.3
+## Date of fit: Thu Nov 19 15:00:11 2020
+## Date of summary: Thu Nov 19 15:00:11 2020
##
## Equations:
## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -528,7 +545,7 @@
##
## Model predictions using solution type analytical
##
-## Fitted using 373 model solutions performed in 0.086 s
+## Fitted using 376 model solutions performed in 0.083 s
##
## Error model: Constant variance
##
@@ -546,7 +563,7 @@
## parent_0 97.800000 -Inf Inf
## log_k1 -2.302585 -Inf Inf
## log_k2 -4.605170 -Inf Inf
-## g_ilr 0.000000 -Inf Inf
+## g_qlogis 0.000000 -Inf Inf
##
## Fixed parameter values:
## None
@@ -561,16 +578,16 @@
## 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
+## g_qlogis -0.1739 0.05270 -0.3416 -0.006142
## 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 -6.868e-07
-## log_k1 1.732e-01 1.000e+00 4.945e-01 -5.809e-01 3.175e-07
-## log_k2 2.282e-02 4.945e-01 1.000e+00 -6.812e-01 7.631e-07
-## g_ilr 4.009e-01 -5.809e-01 -6.812e-01 1.000e+00 -8.694e-07
-## sigma -6.868e-07 3.175e-07 7.631e-07 -8.694e-07 1.000e+00
+## parent_0 log_k1 log_k2 g_qlogis sigma
+## parent_0 1.000e+00 1.732e-01 2.282e-02 4.009e-01 -9.671e-08
+## log_k1 1.732e-01 1.000e+00 4.945e-01 -5.809e-01 7.148e-07
+## log_k2 2.282e-02 4.945e-01 1.000e+00 -6.812e-01 1.022e-06
+## g_qlogis 4.009e-01 -5.809e-01 -6.812e-01 1.000e+00 -7.929e-07
+## sigma -9.671e-08 7.148e-07 1.022e-06 -7.929e-07 1.000e+00
##
## Backtransformed parameters:
## Confidence intervals for internally transformed parameters are asymmetric.
@@ -602,7 +619,8 @@
## 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="cb26"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">mm.L3</span><span class="kw">[[</span><span class="st">"DFOP"</span>, <span class="fl">1</span>]], <span class="kw">show_errmin</span> <span class="kw">=</span> <span class="fl">TRUE</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html">plot</a></span><span class="op">(</span><span class="va">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>
<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>
@@ -612,30 +630,33 @@
<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="cb27"><html><body><pre class="r"><span class="no">FOCUS_2006_L4</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span>(
- <span class="kw">t</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></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="kw">parent</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">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>))
-<span class="no">FOCUS_2006_L4_mkin</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(<span class="no">FOCUS_2006_L4</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb27"><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">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">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">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"><html><body><pre class="r"><span class="co"># Only use one core here, not to offend the CRAN checks</span>
-<span class="no">mm.L4</span> <span class="kw">&lt;-</span> <span class="fu"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>), <span class="kw">cores</span> <span class="kw">=</span> <span class="fl">1</span>,
- <span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="st">"FOCUS L4"</span> <span class="kw">=</span> <span class="no">FOCUS_2006_L4_mkin</span>),
- <span class="kw">quiet</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
-<span class="fu"><a href="https://rdrr.io/r/base/plot.html">plot</a></span>(<span class="no">mm.L4</span>)</pre></body></html></div>
+<div class="sourceCode" id="cb28"><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">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">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>,
+ 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-method.html">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"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">mm.L4</span><span class="kw">[[</span><span class="st">"SFO"</span>, <span class="fl">1</span>]], <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
-<pre><code>## mkin version used for fitting: 0.9.50.3
-## R version used for fitting: 4.0.2
-## Date of fit: Thu Oct 8 09:14:07 2020
-## Date of summary: Thu Oct 8 09:14:07 2020
+<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"SFO"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
+<pre><code>## mkin version used for fitting: 0.9.50.4
+## R version used for fitting: 4.0.3
+## Date of fit: Thu Nov 19 15:00:12 2020
+## Date of summary: Thu Nov 19 15:00:12 2020
##
## Equations:
## d_parent/dt = - k_parent * parent
##
## Model predictions using solution type analytical
##
-## Fitted using 142 model solutions performed in 0.03 s
+## Fitted using 142 model solutions performed in 0.031 s
##
## Error model: Constant variance
##
@@ -688,18 +709,19 @@
## Estimated disappearance times:
## DT50 DT90
## parent 106 352</code></pre>
-<div class="sourceCode" id="cb31"><html><body><pre class="r"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span>(<span class="no">mm.L4</span><span class="kw">[[</span><span class="st">"FOMC"</span>, <span class="fl">1</span>]], <span class="kw">data</span> <span class="kw">=</span> <span class="fl">FALSE</span>)</pre></body></html></div>
-<pre><code>## mkin version used for fitting: 0.9.50.3
-## R version used for fitting: 4.0.2
-## Date of fit: Thu Oct 8 09:14:07 2020
-## Date of summary: Thu Oct 8 09:14:07 2020
+<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html">summary</a></span><span class="op">(</span><span class="va">mm.L4</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="fl">1</span><span class="op">]</span><span class="op">]</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div>
+<pre><code>## mkin version used for fitting: 0.9.50.4
+## R version used for fitting: 4.0.3
+## Date of fit: Thu Nov 19 15:00:12 2020
+## Date of summary: Thu Nov 19 15:00:12 2020
##
## Equations:
## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
##
## Model predictions using solution type analytical
##
-## Fitted using 224 model solutions performed in 0.046 s
+## Fitted using 224 model solutions performed in 0.05 s
##
## Error model: Constant variance
##
@@ -784,7 +806,7 @@
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- <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+ <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
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