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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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<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'><-</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'>#> <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'><-</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'>#> <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'><-</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'>#> <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'><-</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'>#> <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'><-</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'><-</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'><-</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'><-</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$time == 0 & match(d_rep$name, c("M1", "M2"), "value"] <- 0</span>
<span class='co'># d_NA <- transform(d_rep, value = ifelse(value < LOD, NA, value))</span>
<span class='co'># d_NA$value <- round(d_NA$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'><-</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'>#> mkin version used for fitting: 0.9.49.6
#> R version used for fitting: 3.6.1
#> Date of fit: Thu Sep 19 12:43:02 2019
#> Date of summary: Thu Sep 19 12:43:02 2019
#>
#> Equations:
#> d_parent/dt = - k_parent * parent
#> d_M1/dt = + f_parent_to_M1 * k_parent * parent - k_M1 * M1
#> d_M2/dt = + f_M1_to_M2 * k_M1 * M1 - k_M2 * M2
#>
#> Model predictions using solution type deSolve
#>
#> Fitted using 847 model solutions performed in 2.51 s
#>
#> Error model: Constant variance
#>
#> Error model algorithm: OLS
#>
#> Starting values for parameters to be optimised:
#> value type
#> parent_0 101.350000 state
#> k_parent 0.100000 deparm
#> k_M1 0.100100 deparm
#> k_M2 0.100200 deparm
#> f_parent_to_M1 0.500000 deparm
#> f_M1_to_M2 0.500000 deparm
#> sigma 2.273126 error
#>
#> Starting values for the transformed parameters actually optimised:
#> value lower upper
#> parent_0 101.350000 -Inf Inf
#> log_k_parent -2.302585 -Inf Inf
#> log_k_M1 -2.301586 -Inf Inf
#> log_k_M2 -2.300587 -Inf Inf
#> f_parent_ilr_1 0.000000 -Inf Inf
#> f_M1_ilr_1 0.000000 -Inf Inf
#> sigma 2.273126 0 Inf
#>
#> Fixed parameter values:
#> value type
#> M1_0 0 state
#> M2_0 0 state
#>
#> Optimised, transformed parameters with symmetric confidence intervals:
#> Estimate Std. Error Lower Upper
#> parent_0 102.1000 1.57000 98.8600 105.3000
#> log_k_parent -0.3020 0.03885 -0.3812 -0.2229
#> log_k_M1 -1.2070 0.07123 -1.3520 -1.0620
#> log_k_M2 -3.9010 0.06571 -4.0350 -3.7670
#> f_parent_ilr_1 0.8492 0.16640 0.5103 1.1880
#> f_M1_ilr_1 0.6780 0.17600 0.3196 1.0360
#> sigma 2.2730 0.25740 1.7490 2.7970
#>
#> Parameter correlation:
#> parent_0 log_k_parent log_k_M1 log_k_M2 f_parent_ilr_1
#> parent_0 1.000e+00 3.933e-01 -1.605e-01 2.819e-02 -4.624e-01
#> log_k_parent 3.933e-01 1.000e+00 -4.082e-01 7.166e-02 -5.682e-01
#> log_k_M1 -1.605e-01 -4.082e-01 1.000e+00 -3.929e-01 7.478e-01
#> log_k_M2 2.819e-02 7.166e-02 -3.929e-01 1.000e+00 -2.658e-01
#> f_parent_ilr_1 -4.624e-01 -5.682e-01 7.478e-01 -2.658e-01 1.000e+00
#> f_M1_ilr_1 1.614e-01 4.102e-01 -8.109e-01 5.419e-01 -8.605e-01
#> sigma -3.704e-09 -1.104e-08 5.922e-08 -3.673e-08 5.867e-08
#> f_M1_ilr_1 sigma
#> parent_0 1.614e-01 -3.704e-09
#> log_k_parent 4.102e-01 -1.104e-08
#> log_k_M1 -8.109e-01 5.922e-08
#> log_k_M2 5.419e-01 -3.673e-08
#> f_parent_ilr_1 -8.605e-01 5.867e-08
#> f_M1_ilr_1 1.000e+00 -8.075e-08
#> sigma -8.075e-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(>t) Lower Upper
#> parent_0 102.10000 65.000 7.281e-36 98.86000 105.30000
#> k_parent 0.73930 25.740 2.948e-23 0.68310 0.80020
#> k_M1 0.29920 14.040 1.577e-15 0.25880 0.34590
#> k_M2 0.02023 15.220 1.653e-16 0.01769 0.02312
#> f_parent_to_M1 0.76870 18.370 7.295e-19 0.67300 0.84290
#> f_M1_to_M2 0.72290 14.500 6.418e-16 0.61110 0.81240
#> sigma 2.27300 8.832 2.161e-10 1.74900 2.79700
#>
#> FOCUS Chi2 error levels in percent:
#> err.min n.optim df
#> All data 8.454 6 17
#> parent 8.660 2 6
#> M1 10.583 2 5
#> M2 3.586 2 6
#>
#> Resulting formation fractions:
#> ff
#> parent_M1 0.7687
#> parent_sink 0.2313
#> M1_M2 0.7229
#> M1_sink 0.2771
#>
#> Estimated disappearance times:
#> DT50 DT90
#> parent 0.9376 3.114
#> M1 2.3170 7.697
#> M2 34.2689 113.839
#>
#> Data:
#> time variable observed predicted residual
#> 0 parent 101.5 1.021e+02 -0.56248
#> 0 parent 101.2 1.021e+02 -0.86248
#> 1 parent 53.9 4.873e+01 5.17118
#> 1 parent 47.5 4.873e+01 -1.22882
#> 3 parent 10.4 1.111e+01 -0.70773
#> 3 parent 7.6 1.111e+01 -3.50773
#> 7 parent 1.1 5.772e-01 0.52283
#> 7 parent 0.3 5.772e-01 -0.27717
#> 14 parent 3.5 3.264e-03 3.49674
#> 28 parent 3.2 1.045e-07 3.20000
#> 90 parent 0.6 -1.875e-11 0.60000
#> 120 parent 3.5 -2.805e-11 3.50000
#> 1 M1 36.4 3.479e+01 1.61088
#> 1 M1 37.4 3.479e+01 2.61088
#> 3 M1 34.3 3.937e+01 -5.07027
#> 3 M1 39.8 3.937e+01 0.42973
#> 7 M1 15.1 1.549e+01 -0.38715
#> 7 M1 17.8 1.549e+01 2.31285
#> 14 M1 5.8 1.995e+00 3.80469
#> 14 M1 1.2 1.995e+00 -0.79531
#> 60 M1 0.5 2.111e-06 0.50000
#> 90 M1 3.2 2.913e-10 3.20000
#> 120 M1 1.5 3.625e-11 1.50000
#> 120 M1 0.6 3.625e-11 0.60000
#> 1 M2 4.8 4.455e+00 0.34517
#> 3 M2 20.9 2.153e+01 -0.62527
#> 3 M2 19.3 2.153e+01 -2.22527
#> 7 M2 42.0 4.192e+01 0.07941
#> 7 M2 43.1 4.192e+01 1.17941
#> 14 M2 49.4 4.557e+01 3.83353
#> 14 M2 44.3 4.557e+01 -1.26647
#> 28 M2 34.6 3.547e+01 -0.87275
#> 28 M2 33.0 3.547e+01 -2.47275
#> 60 M2 18.8 1.858e+01 0.21837
#> 60 M2 17.6 1.858e+01 -0.98163
#> 90 M2 10.6 1.013e+01 0.47130
#> 90 M2 10.8 1.013e+01 0.67130
#> 120 M2 9.8 5.521e+00 4.27893
#> 120 M2 3.3 5.521e+00 -2.22107</div></pre>
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