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authorJohannes Ranke <jranke@uni-bremen.de>2019-09-19 12:43:04 +0200
committerJohannes Ranke <jranke@uni-bremen.de>2019-09-19 12:43:04 +0200
commita7beb73cdfeed34525266d76f424375e1d069a48 (patch)
tree05539773752db6ee94ccc28dc3521c3916312e41 /docs/reference/synthetic_data_for_UBA_2014.html
parent90ff0d8e5932799b1c704555663a65944b7c4091 (diff)
Static documentation rebuilt by pkgdown
Use lazy = TRUE in the pd target for generating pkgdown documentation
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+<meta property="og:title" content="Synthetic datasets for one parent compound with two metabolites — synthetic_data_for_UBA_2014" />
+
+<meta property="og:description" content="The 12 datasets were generated using four different models and three different
+ variance components. The four models are either the SFO or the DFOP model with either
+ two sequential or two parallel metabolites.
+Variance component 'a' is based on a normal distribution with standard deviation of 3,
+ Variance component 'b' is also based on a normal distribution, but with a standard deviation of 7.
+ Variance component 'c' is based on the error model from Rocke and Lorenzato (1995), with the
+ minimum standard deviation (for small y values) of 0.5, and a proportionality constant of 0.07
+ for the increase of the standard deviation with y. Note that this is a simplified version
+ of the error model proposed by Rocke and Lorenzato (1995), as in their model the error of the
+ measured values approximates lognormal distribution for high values, whereas we are using
+ normally distributed error components all along.
+Initial concentrations for metabolites and all values where adding the variance component resulted
+ in a value below the assumed limit of detection of 0.1 were set to NA.
+As an example, the first dataset has the title SFO_lin_a and is based on the SFO model
+ with two sequential metabolites (linear pathway), with added variance component 'a'.
+Compare also the code in the example section to see the degradation models." />
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+ <div class="page-header">
+ <h1>Synthetic datasets for one parent compound with two metabolites</h1>
+
+ <div class="hidden name"><code>synthetic_data_for_UBA_2014.Rd</code></div>
+ </div>
+
+ <div class="ref-description">
+
+ <p>The 12 datasets were generated using four different models and three different
+ variance components. The four models are either the SFO or the DFOP model with either
+ two sequential or two parallel metabolites.</p>
+<p>Variance component 'a' is based on a normal distribution with standard deviation of 3,
+ Variance component 'b' is also based on a normal distribution, but with a standard deviation of 7.
+ Variance component 'c' is based on the error model from Rocke and Lorenzato (1995), with the
+ minimum standard deviation (for small y values) of 0.5, and a proportionality constant of 0.07
+ for the increase of the standard deviation with y. Note that this is a simplified version
+ of the error model proposed by Rocke and Lorenzato (1995), as in their model the error of the
+ measured values approximates lognormal distribution for high values, whereas we are using
+ normally distributed error components all along.</p>
+<p>Initial concentrations for metabolites and all values where adding the variance component resulted
+ in a value below the assumed limit of detection of 0.1 were set to <code>NA</code>.</p>
+<p>As an example, the first dataset has the title <code>SFO_lin_a</code> and is based on the SFO model
+ with two sequential metabolites (linear pathway), with added variance component 'a'.</p>
+<p>Compare also the code in the example section to see the degradation models.</p>
+
+ </div>
+
+ <pre class="usage"><span class='no'>synthetic_data_for_UBA_2014</span></pre>
+
+ <h2 class="hasAnchor" id="format"><a class="anchor" href="#format"></a>Format</h2>
+
+ <p>A list containing twelve datasets as an R6 class defined by <code><a href='mkinds.html'>mkinds</a></code>,
+ each containing, among others, the following components</p><dl class='dl-horizontal'>
+ <dt><code>title</code></dt><dd><p>The name of the dataset, e.g. <code>SFO_lin_a</code></p></dd>
+ <dt><code>data</code></dt><dd><p>A data frame with the data in the form expected by <code><a href='mkinfit.html'>mkinfit</a></code></p></dd>
+
+</dl>
+
+
+ <h2 class="hasAnchor" id="source"><a class="anchor" href="#source"></a>Source</h2>
+
+ <p>Ranke (2014) Prüfung und Validierung von Modellierungssoftware als Alternative
+ zu ModelMaker 4.0, Umweltbundesamt Projektnummer 27452</p>
+<p>Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for
+ measurement error in analytical chemistry. Technometrics 37(2), 176-184.</p>
+
+
+ <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
+ <pre class="examples"><div class='input'><span class='co'># The data have been generated using the following kinetic models</span>
+<span class='no'>m_synth_SFO_lin</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M1"</span>),
+ <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M2"</span>),
+ <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+
+<span class='no'>m_synth_SFO_par</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>),
+ <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>),
+ <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>),
+ <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='no'>m_synth_DFOP_lin</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"DFOP"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M1"</span>),
+ <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M2"</span>),
+ <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='no'>m_synth_DFOP_par</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"DFOP"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>),
+ <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>),
+ <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>),
+ <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
+<span class='co'># The model predictions without intentional error were generated as follows</span>
+<span class='no'>sampling_times</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'>1</span>, <span class='fl'>3</span>, <span class='fl'>7</span>, <span class='fl'>14</span>, <span class='fl'>28</span>, <span class='fl'>60</span>, <span class='fl'>90</span>, <span class='fl'>120</span>)
+
+<span class='no'>d_synth_SFO_lin</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>m_synth_SFO_lin</span>,
+ <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_parent</span> <span class='kw'>=</span> <span class='fl'>0.7</span>, <span class='kw'>f_parent_to_M1</span> <span class='kw'>=</span> <span class='fl'>0.8</span>,
+ <span class='kw'>k_M1</span> <span class='kw'>=</span> <span class='fl'>0.3</span>, <span class='kw'>f_M1_to_M2</span> <span class='kw'>=</span> <span class='fl'>0.7</span>,
+ <span class='kw'>k_M2</span> <span class='kw'>=</span> <span class='fl'>0.02</span>),
+ <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fl'>0</span>),
+ <span class='no'>sampling_times</span>)
+
+<span class='no'>d_synth_DFOP_lin</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>m_synth_DFOP_lin</span>,
+ <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k1</span> <span class='kw'>=</span> <span class='fl'>0.2</span>, <span class='kw'>k2</span> <span class='kw'>=</span> <span class='fl'>0.02</span>, <span class='kw'>g</span> <span class='kw'>=</span> <span class='fl'>0.5</span>,
+ <span class='kw'>f_parent_to_M1</span> <span class='kw'>=</span> <span class='fl'>0.5</span>, <span class='kw'>k_M1</span> <span class='kw'>=</span> <span class='fl'>0.3</span>,
+ <span class='kw'>f_M1_to_M2</span> <span class='kw'>=</span> <span class='fl'>0.7</span>, <span class='kw'>k_M2</span> <span class='kw'>=</span> <span class='fl'>0.02</span>),
+ <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fl'>0</span>),
+ <span class='no'>sampling_times</span>)
+
+<span class='no'>d_synth_SFO_par</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>m_synth_SFO_par</span>,
+ <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k_parent</span> <span class='kw'>=</span> <span class='fl'>0.2</span>,
+ <span class='kw'>f_parent_to_M1</span> <span class='kw'>=</span> <span class='fl'>0.8</span>, <span class='kw'>k_M1</span> <span class='kw'>=</span> <span class='fl'>0.01</span>,
+ <span class='kw'>f_parent_to_M2</span> <span class='kw'>=</span> <span class='fl'>0.2</span>, <span class='kw'>k_M2</span> <span class='kw'>=</span> <span class='fl'>0.02</span>),
+ <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fl'>0</span>),
+ <span class='no'>sampling_times</span>)
+
+<span class='no'>d_synth_DFOP_par</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>m_synth_DFOP_par</span>,
+ <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>k1</span> <span class='kw'>=</span> <span class='fl'>0.3</span>, <span class='kw'>k2</span> <span class='kw'>=</span> <span class='fl'>0.02</span>, <span class='kw'>g</span> <span class='kw'>=</span> <span class='fl'>0.7</span>,
+ <span class='kw'>f_parent_to_M1</span> <span class='kw'>=</span> <span class='fl'>0.6</span>, <span class='kw'>k_M1</span> <span class='kw'>=</span> <span class='fl'>0.04</span>,
+ <span class='kw'>f_parent_to_M2</span> <span class='kw'>=</span> <span class='fl'>0.4</span>, <span class='kw'>k_M2</span> <span class='kw'>=</span> <span class='fl'>0.01</span>),
+ <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fl'>0</span>),
+ <span class='no'>sampling_times</span>)
+
+<span class='co'># Construct names for datasets with errors</span>
+<span class='no'>d_synth_names</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste0</a></span>(<span class='st'>"d_synth_"</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"SFO_lin"</span>, <span class='st'>"SFO_par"</span>,
+ <span class='st'>"DFOP_lin"</span>, <span class='st'>"DFOP_par"</span>))
+
+<span class='co'># Original function used or adding errors. The add_err function now published</span>
+<span class='co'># with this package is a slightly generalised version where the names of</span>
+<span class='co'># secondary compartments that should have an initial value of zero (M1 and M2</span>
+<span class='co'># in this case) are not hardcoded any more.</span>
+<span class='co'># add_err = function(d, sdfunc, LOD = 0.1, reps = 2, seed = 123456789)</span>
+<span class='co'># {</span>
+<span class='co'># set.seed(seed)</span>
+<span class='co'># d_long = mkin_wide_to_long(d, time = "time")</span>
+<span class='co'># d_rep = data.frame(lapply(d_long, rep, each = 2))</span>
+<span class='co'># d_rep$value = rnorm(length(d_rep$value), d_rep$value, sdfunc(d_rep$value))</span>
+<span class='co'>#</span>
+<span class='co'># d_rep[d_rep$time == 0 &amp; match(d_rep$name, c("M1", "M2"), "value"] &lt;- 0</span>
+<span class='co'># d_NA &lt;- transform(d_rep, value = ifelse(value &lt; LOD, NA, value))</span>
+<span class='co'># d_NA$value &lt;- round(d_NA$value, 1)</span>
+<span class='co'># return(d_NA)</span>
+<span class='co'># }</span>
+
+<span class='co'># The following is the simplified version of the two-component model of Rocke</span>
+<span class='co'># and Lorenzato (1995)</span>
+<span class='no'>sdfunc_twocomp</span> <span class='kw'>=</span> <span class='kw'>function</span>(<span class='no'>value</span>, <span class='no'>sd_low</span>, <span class='no'>rsd_high</span>) {
+ <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>sqrt</a></span>(<span class='no'>sd_low</span>^<span class='fl'>2</span> + <span class='no'>value</span>^<span class='fl'>2</span> * <span class='no'>rsd_high</span>^<span class='fl'>2</span>)
+}
+
+<span class='co'># Add the errors.</span>
+<span class='kw'>for</span> (<span class='no'>d_synth_name</span> <span class='kw'>in</span> <span class='no'>d_synth_names</span>)
+{
+ <span class='no'>d_synth</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/get.html'>get</a></span>(<span class='no'>d_synth_name</span>)
+ <span class='fu'><a href='https://rdrr.io/r/base/assign.html'>assign</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste0</a></span>(<span class='no'>d_synth_name</span>, <span class='st'>"_a"</span>), <span class='fu'><a href='add_err.html'>add_err</a></span>(<span class='no'>d_synth</span>, <span class='kw'>function</span>(<span class='no'>value</span>) <span class='fl'>3</span>))
+ <span class='fu'><a href='https://rdrr.io/r/base/assign.html'>assign</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste0</a></span>(<span class='no'>d_synth_name</span>, <span class='st'>"_b"</span>), <span class='fu'><a href='add_err.html'>add_err</a></span>(<span class='no'>d_synth</span>, <span class='kw'>function</span>(<span class='no'>value</span>) <span class='fl'>7</span>))
+ <span class='fu'><a href='https://rdrr.io/r/base/assign.html'>assign</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste0</a></span>(<span class='no'>d_synth_name</span>, <span class='st'>"_c"</span>), <span class='fu'><a href='add_err.html'>add_err</a></span>(<span class='no'>d_synth</span>,
+ <span class='kw'>function</span>(<span class='no'>value</span>) <span class='fu'>sdfunc_twocomp</span>(<span class='no'>value</span>, <span class='fl'>0.5</span>, <span class='fl'>0.07</span>)))
+
+}
+
+<span class='no'>d_synth_err_names</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(
+ <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/rep.html'>rep</a></span>(<span class='no'>d_synth_names</span>, <span class='kw'>each</span> <span class='kw'>=</span> <span class='fl'>3</span>), <span class='no'>letters</span>[<span class='fl'>1</span>:<span class='fl'>3</span>], <span class='kw'>sep</span> <span class='kw'>=</span> <span class='st'>"_"</span>)
+)
+
+<span class='co'># This is just one example of an evaluation using the kinetic model used for</span>
+<span class='co'># the generation of the data</span>
+<span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>m_synth_SFO_lin</span>, <span class='no'>synthetic_data_for_UBA_2014</span><span class='kw'>[[</span><span class='fl'>1</span>]]$<span class='no'>data</span>,
+ <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
+<span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span>(<span class='no'>fit</span>)</div><div class='img'><img src='synthetic_data_for_UBA_2014-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>fit</span>)</div><div class='output co'>#&gt; mkin version used for fitting: 0.9.49.6
+#&gt; R version used for fitting: 3.6.1
+#&gt; Date of fit: Thu Sep 19 12:43:02 2019
+#&gt; Date of summary: Thu Sep 19 12:43:02 2019
+#&gt;
+#&gt; Equations:
+#&gt; d_parent/dt = - k_parent * parent
+#&gt; d_M1/dt = + f_parent_to_M1 * k_parent * parent - k_M1 * M1
+#&gt; d_M2/dt = + f_M1_to_M2 * k_M1 * M1 - k_M2 * M2
+#&gt;
+#&gt; Model predictions using solution type deSolve
+#&gt;
+#&gt; Fitted using 847 model solutions performed in 2.51 s
+#&gt;
+#&gt; Error model: Constant variance
+#&gt;
+#&gt; Error model algorithm: OLS
+#&gt;
+#&gt; Starting values for parameters to be optimised:
+#&gt; value type
+#&gt; parent_0 101.350000 state
+#&gt; k_parent 0.100000 deparm
+#&gt; k_M1 0.100100 deparm
+#&gt; k_M2 0.100200 deparm
+#&gt; f_parent_to_M1 0.500000 deparm
+#&gt; f_M1_to_M2 0.500000 deparm
+#&gt; sigma 2.273126 error
+#&gt;
+#&gt; Starting values for the transformed parameters actually optimised:
+#&gt; value lower upper
+#&gt; parent_0 101.350000 -Inf Inf
+#&gt; log_k_parent -2.302585 -Inf Inf
+#&gt; log_k_M1 -2.301586 -Inf Inf
+#&gt; log_k_M2 -2.300587 -Inf Inf
+#&gt; f_parent_ilr_1 0.000000 -Inf Inf
+#&gt; f_M1_ilr_1 0.000000 -Inf Inf
+#&gt; sigma 2.273126 0 Inf
+#&gt;
+#&gt; Fixed parameter values:
+#&gt; value type
+#&gt; M1_0 0 state
+#&gt; M2_0 0 state
+#&gt;
+#&gt; Optimised, transformed parameters with symmetric confidence intervals:
+#&gt; Estimate Std. Error Lower Upper
+#&gt; parent_0 102.1000 1.57000 98.8600 105.3000
+#&gt; log_k_parent -0.3020 0.03885 -0.3812 -0.2229
+#&gt; log_k_M1 -1.2070 0.07123 -1.3520 -1.0620
+#&gt; log_k_M2 -3.9010 0.06571 -4.0350 -3.7670
+#&gt; f_parent_ilr_1 0.8492 0.16640 0.5103 1.1880
+#&gt; f_M1_ilr_1 0.6780 0.17600 0.3196 1.0360
+#&gt; sigma 2.2730 0.25740 1.7490 2.7970
+#&gt;
+#&gt; Parameter correlation:
+#&gt; parent_0 log_k_parent log_k_M1 log_k_M2 f_parent_ilr_1
+#&gt; parent_0 1.000e+00 3.933e-01 -1.605e-01 2.819e-02 -4.624e-01
+#&gt; log_k_parent 3.933e-01 1.000e+00 -4.082e-01 7.166e-02 -5.682e-01
+#&gt; log_k_M1 -1.605e-01 -4.082e-01 1.000e+00 -3.929e-01 7.478e-01
+#&gt; log_k_M2 2.819e-02 7.166e-02 -3.929e-01 1.000e+00 -2.658e-01
+#&gt; f_parent_ilr_1 -4.624e-01 -5.682e-01 7.478e-01 -2.658e-01 1.000e+00
+#&gt; f_M1_ilr_1 1.614e-01 4.102e-01 -8.109e-01 5.419e-01 -8.605e-01
+#&gt; sigma -3.704e-09 -1.104e-08 5.922e-08 -3.673e-08 5.867e-08
+#&gt; f_M1_ilr_1 sigma
+#&gt; parent_0 1.614e-01 -3.704e-09
+#&gt; log_k_parent 4.102e-01 -1.104e-08
+#&gt; log_k_M1 -8.109e-01 5.922e-08
+#&gt; log_k_M2 5.419e-01 -3.673e-08
+#&gt; f_parent_ilr_1 -8.605e-01 5.867e-08
+#&gt; f_M1_ilr_1 1.000e+00 -8.075e-08
+#&gt; sigma -8.075e-08 1.000e+00
+#&gt;
+#&gt; Backtransformed parameters:
+#&gt; Confidence intervals for internally transformed parameters are asymmetric.
+#&gt; t-test (unrealistically) based on the assumption of normal distribution
+#&gt; for estimators of untransformed parameters.
+#&gt; Estimate t value Pr(&gt;t) Lower Upper
+#&gt; parent_0 102.10000 65.000 7.281e-36 98.86000 105.30000
+#&gt; k_parent 0.73930 25.740 2.948e-23 0.68310 0.80020
+#&gt; k_M1 0.29920 14.040 1.577e-15 0.25880 0.34590
+#&gt; k_M2 0.02023 15.220 1.653e-16 0.01769 0.02312
+#&gt; f_parent_to_M1 0.76870 18.370 7.295e-19 0.67300 0.84290
+#&gt; f_M1_to_M2 0.72290 14.500 6.418e-16 0.61110 0.81240
+#&gt; sigma 2.27300 8.832 2.161e-10 1.74900 2.79700
+#&gt;
+#&gt; FOCUS Chi2 error levels in percent:
+#&gt; err.min n.optim df
+#&gt; All data 8.454 6 17
+#&gt; parent 8.660 2 6
+#&gt; M1 10.583 2 5
+#&gt; M2 3.586 2 6
+#&gt;
+#&gt; Resulting formation fractions:
+#&gt; ff
+#&gt; parent_M1 0.7687
+#&gt; parent_sink 0.2313
+#&gt; M1_M2 0.7229
+#&gt; M1_sink 0.2771
+#&gt;
+#&gt; Estimated disappearance times:
+#&gt; DT50 DT90
+#&gt; parent 0.9376 3.114
+#&gt; M1 2.3170 7.697
+#&gt; M2 34.2689 113.839
+#&gt;
+#&gt; Data:
+#&gt; time variable observed predicted residual
+#&gt; 0 parent 101.5 1.021e+02 -0.56248
+#&gt; 0 parent 101.2 1.021e+02 -0.86248
+#&gt; 1 parent 53.9 4.873e+01 5.17118
+#&gt; 1 parent 47.5 4.873e+01 -1.22882
+#&gt; 3 parent 10.4 1.111e+01 -0.70773
+#&gt; 3 parent 7.6 1.111e+01 -3.50773
+#&gt; 7 parent 1.1 5.772e-01 0.52283
+#&gt; 7 parent 0.3 5.772e-01 -0.27717
+#&gt; 14 parent 3.5 3.264e-03 3.49674
+#&gt; 28 parent 3.2 1.045e-07 3.20000
+#&gt; 90 parent 0.6 -1.875e-11 0.60000
+#&gt; 120 parent 3.5 -2.805e-11 3.50000
+#&gt; 1 M1 36.4 3.479e+01 1.61088
+#&gt; 1 M1 37.4 3.479e+01 2.61088
+#&gt; 3 M1 34.3 3.937e+01 -5.07027
+#&gt; 3 M1 39.8 3.937e+01 0.42973
+#&gt; 7 M1 15.1 1.549e+01 -0.38715
+#&gt; 7 M1 17.8 1.549e+01 2.31285
+#&gt; 14 M1 5.8 1.995e+00 3.80469
+#&gt; 14 M1 1.2 1.995e+00 -0.79531
+#&gt; 60 M1 0.5 2.111e-06 0.50000
+#&gt; 90 M1 3.2 2.913e-10 3.20000
+#&gt; 120 M1 1.5 3.625e-11 1.50000
+#&gt; 120 M1 0.6 3.625e-11 0.60000
+#&gt; 1 M2 4.8 4.455e+00 0.34517
+#&gt; 3 M2 20.9 2.153e+01 -0.62527
+#&gt; 3 M2 19.3 2.153e+01 -2.22527
+#&gt; 7 M2 42.0 4.192e+01 0.07941
+#&gt; 7 M2 43.1 4.192e+01 1.17941
+#&gt; 14 M2 49.4 4.557e+01 3.83353
+#&gt; 14 M2 44.3 4.557e+01 -1.26647
+#&gt; 28 M2 34.6 3.547e+01 -0.87275
+#&gt; 28 M2 33.0 3.547e+01 -2.47275
+#&gt; 60 M2 18.8 1.858e+01 0.21837
+#&gt; 60 M2 17.6 1.858e+01 -0.98163
+#&gt; 90 M2 10.6 1.013e+01 0.47130
+#&gt; 90 M2 10.8 1.013e+01 0.67130
+#&gt; 120 M2 9.8 5.521e+00 4.27893
+#&gt; 120 M2 3.3 5.521e+00 -2.22107</div></pre>
+ </div>
+ <div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
+ <h2>Contents</h2>
+ <ul class="nav nav-pills nav-stacked">
+
+ <li><a href="#format">Format</a></li>
+
+ <li><a href="#source">Source</a></li>
+
+ <li><a href="#examples">Examples</a></li>
+ </ul>
+
+ </div>
+</div>
+
+
+ <footer>
+ <div class="copyright">
+ <p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown">
+ <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.4.1.</p>
+</div>
+
+ </footer>
+ </div>
+
+
+
+
+ </body>
+</html>
+
+

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