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<h1>Fit nonlinear mixed models with SAEM</h1>
<small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/saemix.R'><code>R/saemix.R</code></a></small>
<div class="hidden name"><code>saem.Rd</code></div>
</div>
<div class="ref-description">
<p>This function uses <code><a href='https://rdrr.io/pkg/saemix/man/saemix.html'>saemix::saemix()</a></code> as a backend for fitting nonlinear mixed
effects models created from <a href='mmkin.html'>mmkin</a> row objects using the Stochastic Approximation
Expectation Maximisation algorithm (SAEM).</p>
</div>
<pre class="usage"><span class='fu'>saem</span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>control</span>, <span class='va'>...</span><span class='op'>)</span>
<span class='co'># S3 method for mmkin</span>
<span class='fu'>saem</span><span class='op'>(</span>
<span class='va'>object</span>,
control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>displayProgress <span class='op'>=</span> <span class='cn'>FALSE</span>, print <span class='op'>=</span> <span class='cn'>FALSE</span>, save <span class='op'>=</span> <span class='cn'>FALSE</span>, save.graphs <span class='op'>=</span>
<span class='cn'>FALSE</span><span class='op'>)</span>,
cores <span class='op'>=</span> <span class='fl'>1</span>,
verbose <span class='op'>=</span> <span class='cn'>FALSE</span>,
suppressPlot <span class='op'>=</span> <span class='cn'>TRUE</span>,
<span class='va'>...</span>
<span class='op'>)</span>
<span class='co'># S3 method for saem.mmkin</span>
<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>x</span>, digits <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Extremes.html'>max</a></span><span class='op'>(</span><span class='fl'>3</span>, <span class='fu'><a href='https://rdrr.io/r/base/options.html'>getOption</a></span><span class='op'>(</span><span class='st'>"digits"</span><span class='op'>)</span> <span class='op'>-</span> <span class='fl'>3</span><span class='op'>)</span>, <span class='va'>...</span><span class='op'>)</span>
<span class='fu'>saemix_model</span><span class='op'>(</span><span class='va'>object</span>, cores <span class='op'>=</span> <span class='fl'>1</span>, verbose <span class='op'>=</span> <span class='cn'>FALSE</span>, <span class='va'>...</span><span class='op'>)</span>
<span class='fu'>saemix_data</span><span class='op'>(</span><span class='va'>object</span>, verbose <span class='op'>=</span> <span class='cn'>FALSE</span>, <span class='va'>...</span><span class='op'>)</span></pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>object</th>
<td><p>An <a href='mmkin.html'>mmkin</a> row object containing several fits of the same
<a href='mkinmod.html'>mkinmod</a> model to different datasets</p></td>
</tr>
<tr>
<th>control</th>
<td><p>Passed to <a href='https://rdrr.io/pkg/saemix/man/saemix.html'>saemix::saemix</a></p></td>
</tr>
<tr>
<th>...</th>
<td><p>Further parameters passed to <a href='https://rdrr.io/pkg/saemix/man/saemixData.html'>saemix::saemixData</a>
and <a href='https://rdrr.io/pkg/saemix/man/saemixModel.html'>saemix::saemixModel</a>.</p></td>
</tr>
<tr>
<th>cores</th>
<td><p>The number of cores to be used for multicore processing using
<code><a href='https://rdrr.io/r/parallel/mclapply.html'>parallel::mclapply()</a></code>. Using more than 1 core is experimental and may
lead to uncontrolled forking, apparently depending on the BLAS version
used.</p></td>
</tr>
<tr>
<th>verbose</th>
<td><p>Should we print information about created objects?</p></td>
</tr>
<tr>
<th>suppressPlot</th>
<td><p>Should we suppress any plotting that is done
by the saemix function?</p></td>
</tr>
<tr>
<th>x</th>
<td><p>An saem.mmkin object to print</p></td>
</tr>
<tr>
<th>digits</th>
<td><p>Number of digits to use for printing</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>An S3 object of class 'saem.mmkin', containing the fitted
<a href='https://rdrr.io/pkg/saemix/man/SaemixObject-class.html'>saemix::SaemixObject</a> as a list component named 'so'. The
object also inherits from 'mixed.mmkin'.</p>
<p>An <a href='https://rdrr.io/pkg/saemix/man/SaemixModel-class.html'>saemix::SaemixModel</a> object.</p>
<p>An <a href='https://rdrr.io/pkg/saemix/man/SaemixData-class.html'>saemix::SaemixData</a> object.</p>
<h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
<p>An mmkin row object is essentially a list of mkinfit objects that have been
obtained by fitting the same model to a list of datasets using <a href='mkinfit.html'>mkinfit</a>.</p>
<p>Starting values for the fixed effects (population mean parameters, argument
psi0 of <code><a href='https://rdrr.io/pkg/saemix/man/saemixModel.html'>saemix::saemixModel()</a></code> are the mean values of the parameters found
using <a href='mmkin.html'>mmkin</a>.</p>
<h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
<div class='dont-index'><p><a href='summary.saem.mmkin.html'>summary.saem.mmkin</a> <a href='plot.mixed.mmkin.html'>plot.mixed.mmkin</a></p></div>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='co'># \dontrun{</span>
<span class='va'>ds</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>experimental_data_for_UBA_2019</span><span class='op'>[</span><span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>]</span>,
<span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>x</span><span class='op'>$</span><span class='va'>data</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'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span><span class='op'>)</span><span class='op'>]</span><span class='op'>)</span><span class='op'>)</span>
<span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>ds</span><span class='op'>)</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span><span class='op'>(</span><span class='st'>"Dataset"</span>, <span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>)</span>
<span class='va'>f_mmkin_parent_p0_fixed</span> <span class='op'><-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='va'>ds</span>, cores <span class='op'>=</span> <span class='fl'>1</span>,
state.ini <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, fixed_initials <span class='op'>=</span> <span class='st'>"parent"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='va'>f_saem_p0_fixed</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent_p0_fixed</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Wed Nov 11 09:36:41 2020"
#> ....
#> Minimisation finished
#> [1] "Wed Nov 11 09:36:43 2020"</div><div class='input'>
<span class='va'>f_mmkin_parent</span> <span class='op'><-</span> <span class='fu'><a href='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>, <span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='va'>f_saem_sfo</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent</span><span class='op'>[</span><span class='st'>"SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Wed Nov 11 09:36:44 2020"
#> ....
#> Minimisation finished
#> [1] "Wed Nov 11 09:36:45 2020"</div><div class='input'><span class='va'>f_saem_fomc</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent</span><span class='op'>[</span><span class='st'>"FOMC"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Wed Nov 11 09:36:46 2020"
#> ....
#> Minimisation finished
#> [1] "Wed Nov 11 09:36:48 2020"</div><div class='input'><span class='va'>f_saem_dfop</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent</span><span class='op'>[</span><span class='st'>"DFOP"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Wed Nov 11 09:36:48 2020"
#> ....
#> Minimisation finished
#> [1] "Wed Nov 11 09:36:51 2020"</div><div class='input'>
<span class='co'># The returned saem.mmkin object contains an SaemixObject, therefore we can use</span>
<span class='co'># functions from saemix</span>
<span class='kw'><a href='https://rdrr.io/r/base/library.html'>library</a></span><span class='op'>(</span><span class='va'>saemix</span><span class='op'>)</span>
</div><div class='output co'>#> <span class='message'>Package saemix, version 3.1.9000</span>
#> <span class='message'> please direct bugs, questions and feedback to emmanuelle.comets@inserm.fr</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/compare.saemix.html'>compare.saemix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='va'>f_saem_sfo</span><span class='op'>$</span><span class='va'>so</span>, <span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, <span class='va'>f_saem_dfop</span><span class='op'>$</span><span class='va'>so</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#> Likelihoods computed by importance sampling </div><div class='output co'>#> AIC BIC
#> 1 624.2484 622.2956
#> 2 467.7096 464.9757
#> 3 495.4373 491.9222</div><div class='input'><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'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"convergence"</span><span class='op'>)</span>
</div><div class='output co'>#> Plotting convergence plots</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"individual.fit"</span><span class='op'>)</span>
</div><div class='img'><img src='saem-1.png' alt='' width='700' height='433' /></div><div class='output co'>#> Plotting individual fits</div><div class='input'><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'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"npde"</span><span class='op'>)</span>
</div><div class='img'><img src='saem-2.png' alt='' width='700' height='433' /></div><div class='output co'>#> Simulating data using nsim = 1000 simulated datasets
#> Computing WRES and npde .
#> Plotting npde</div><div class='img'><img src='saem-3.png' alt='' width='700' height='433' /></div><div class='output co'>#> ---------------------------------------------
#> Distribution of npde:
#> mean= -0.01528 (SE= 0.098 )
#> variance= 0.862 (SE= 0.13 )
#> skewness= 0.5016
#> kurtosis= 1.18
#> ---------------------------------------------
#>
#> Statistical tests
#> Wilcoxon signed rank test : 0.679
#> Fisher variance test : 0.36
#> SW test of normality : 0.0855 .
#> Global adjusted p-value : 0.257
#> ---
#> Signif. codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1
#> ---------------------------------------------</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/plot-SaemixObject-method.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, plot.type <span class='op'>=</span> <span class='st'>"vpc"</span><span class='op'>)</span>
</div><div class='output co'>#> Performing simulations under the model.
#> Plotting VPC
#> Method used for VPC: binning by quantiles on X , dividing into the following intervals
#> Interval Centered.On
#> 1 (-1,3] 1.3
#> 2 (3,8] 7.4
#> 3 (8,14] 13.2
#> 4 (14,21] 20.5
#> 5 (21,37.7] 29.5
#> 6 (37.7,60] 50.4
#> 7 (60,90] 76.6
#> 8 (90,120] 109.0
#> 9 (120,180] 156.0 </div><div class='img'><img src='saem-4.png' alt='' width='700' height='433' /></div><div class='input'>
<span class='va'>f_mmkin_parent_tc</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/update.html'>update</a></span><span class='op'>(</span><span class='va'>f_mmkin_parent</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
<span class='va'>f_saem_fomc_tc</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin_parent_tc</span><span class='op'>[</span><span class='st'>"FOMC"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Wed Nov 11 09:36:54 2020"
#> ....
#> Minimisation finished
#> [1] "Wed Nov 11 09:36:59 2020"</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/compare.saemix.html'>compare.saemix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='va'>f_saem_fomc</span><span class='op'>$</span><span class='va'>so</span>, <span class='va'>f_saem_fomc_tc</span><span class='op'>$</span><span class='va'>so</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#> Likelihoods computed by importance sampling </div><div class='output co'>#> AIC BIC
#> 1 467.7096 464.9757
#> 2 469.5208 466.3963</div><div class='input'>
<span class='va'>sfo_sfo</span> <span class='op'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
A1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</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='va'>fomc_sfo</span> <span class='op'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
A1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</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='va'>dfop_sfo</span> <span class='op'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
A1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</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 following fit uses analytical solutions for SFO-SFO and DFOP-SFO,</span>
<span class='co'># and compiled ODEs for FOMC, both are fast</span>
<span class='va'>f_mmkin</span> <span class='op'><-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>
<span class='st'>"SFO-SFO"</span> <span class='op'>=</span> <span class='va'>sfo_sfo</span>, <span class='st'>"FOMC-SFO"</span> <span class='op'>=</span> <span class='va'>fomc_sfo</span>, <span class='st'>"DFOP-SFO"</span> <span class='op'>=</span> <span class='va'>dfop_sfo</span><span class='op'>)</span>,
<span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='co'># These take about five seconds each on this system, as we use</span>
<span class='co'># analytical solutions written for saemix. When using the analytical</span>
<span class='co'># solutions written for mkin this took around four minutes</span>
<span class='va'>f_saem_sfo_sfo</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin</span><span class='op'>[</span><span class='st'>"SFO-SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Wed Nov 11 09:37:01 2020"
#> ....
#> Minimisation finished
#> [1] "Wed Nov 11 09:37:06 2020"</div><div class='input'><span class='va'>f_saem_dfop_sfo</span> <span class='op'><-</span> <span class='fu'>saem</span><span class='op'>(</span><span class='va'>f_mmkin</span><span class='op'>[</span><span class='st'>"DFOP-SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Wed Nov 11 09:37:06 2020"
#> ....
#> Minimisation finished
#> [1] "Wed Nov 11 09:37:15 2020"</div><div class='input'><span class='co'># We can use print, plot and summary methods to check the results</span>
<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>f_saem_dfop_sfo</span><span class='op'>)</span>
</div><div class='output co'>#> Kinetic nonlinear mixed-effects model fit by SAEM
#> Structural model:
#> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
#> time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
#> * parent
#> d_A1/dt = + f_parent_to_A1 * ((k1 * g * exp(-k1 * time) + k2 * (1 - g)
#> * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
#> exp(-k2 * time))) * parent - k_A1 * A1
#>
#> Data:
#> 170 observations of 2 variable(s) grouped in 5 datasets
#>
#> Likelihood computed by importance sampling
#>
#> LL by is "-407.78 (df=13)"
#> AIC BIC logLik
#> 841.6 836.5 -407.8
#>
#> Fitted parameters:
#> estimate lower upper
#> parent_0 93.76647 91.15312 96.3798
#> log_k_A1 -6.13235 -8.45788 -3.8068
#> f_parent_qlogis -0.97364 -1.36940 -0.5779
#> log_k1 -2.53176 -3.80372 -1.2598
#> log_k2 -3.58667 -5.29524 -1.8781
#> g_qlogis 0.01238 -1.07968 1.1044
#> Var.parent_0 7.61106 -3.34955 18.5717
#> Var.log_k_A1 4.64679 -2.73133 12.0249
#> Var.f_parent_qlogis 0.19693 -0.05498 0.4488
#> Var.log_k1 2.01717 -0.51980 4.5542
#> Var.log_k2 3.63412 -0.92964 8.1979
#> Var.g_qlogis 0.20045 -0.97425 1.3751
#> a.1 1.88335 1.66636 2.1004
#> SD.parent_0 2.75881 0.77234 4.7453
#> SD.log_k_A1 2.15564 0.44429 3.8670
#> SD.f_parent_qlogis 0.44377 0.15994 0.7276
#> SD.log_k1 1.42027 0.52714 2.3134
#> SD.log_k2 1.90634 0.70934 3.1033
#> SD.g_qlogis 0.44771 -0.86417 1.7596</div><div class='input'><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'>f_saem_dfop_sfo</span><span class='op'>)</span>
</div><div class='img'><img src='saem-5.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/summary-methods.html'>summary</a></span><span class='op'>(</span><span class='va'>f_saem_dfop_sfo</span>, data <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
</div><div class='output co'>#>
#> LL by is "-407.78 (df=13)"</div><div class='output co'>#> saemix version used for fitting: 3.1.9000
#> mkin version used for pre-fitting: 0.9.50.4
#> R version used for fitting: 4.0.3
#> Date of fit: Wed Nov 11 09:37:16 2020
#> Date of summary: Wed Nov 11 09:37:16 2020
#>
#> Equations:
#> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
#> time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
#> * parent
#> d_A1/dt = + f_parent_to_A1 * ((k1 * g * exp(-k1 * time) + k2 * (1 - g)
#> * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
#> exp(-k2 * time))) * parent - k_A1 * A1
#>
#> Data:
#> 170 observations of 2 variable(s) grouped in 5 datasets
#>
#> Model predictions using solution type analytical
#>
#> Fitted in 9.691 s using 300, 100 iterations
#>
#> Variance model: Constant variance
#>
#> Mean of starting values for individual parameters:
#> parent_0 log_k_A1 f_parent_qlogis log_k1 log_k2
#> 93.8101519 -9.7647455 -0.9711148 -1.8799371 -4.2708142
#> g_qlogis
#> 0.1356441
#>
#> Fixed degradation parameter values:
#> None
#>
#> Results:
#>
#> Likelihood computed by importance sampling
#> AIC BIC logLik
#> 841.6 836.5 -407.8
#>
#> Optimised, transformed parameters with symmetric confidence intervals:
#> est. lower upper
#> parent_0 93.76647 91.153 96.3798
#> log_k_A1 -6.13235 -8.458 -3.8068
#> f_parent_qlogis -0.97364 -1.369 -0.5779
#> log_k1 -2.53176 -3.804 -1.2598
#> log_k2 -3.58667 -5.295 -1.8781
#> g_qlogis 0.01238 -1.080 1.1044
#>
#> Correlation:
#> prnt_0 lg__A1 f_prn_ log_k1 log_k2
#> log_k_A1 -0.013
#> f_parent_qlogis -0.025 0.050
#> log_k1 0.030 0.000 -0.005
#> log_k2 0.010 0.005 -0.003 0.032
#> g_qlogis -0.063 -0.015 0.010 -0.167 -0.177
#>
#> Random effects:
#> est. lower upper
#> SD.parent_0 2.7588 0.7723 4.7453
#> SD.log_k_A1 2.1556 0.4443 3.8670
#> SD.f_parent_qlogis 0.4438 0.1599 0.7276
#> SD.log_k1 1.4203 0.5271 2.3134
#> SD.log_k2 1.9063 0.7093 3.1033
#> SD.g_qlogis 0.4477 -0.8642 1.7596
#>
#> Variance model:
#> est. lower upper
#> a.1 1.883 1.666 2.1
#>
#> Backtransformed parameters with asymmetric confidence intervals:
#> est. lower upper
#> parent_0 93.766473 9.115e+01 96.37983
#> k_A1 0.002171 2.122e-04 0.02222
#> f_parent_to_A1 0.274156 2.027e-01 0.35942
#> k1 0.079519 2.229e-02 0.28371
#> k2 0.027691 5.015e-03 0.15288
#> g 0.503095 2.536e-01 0.75109
#>
#> Resulting formation fractions:
#> ff
#> parent_A1 0.2742
#> parent_sink 0.7258
#>
#> Estimated disappearance times:
#> DT50 DT90 DT50back DT50_k1 DT50_k2
#> parent 14.11 59.53 17.92 8.717 25.03
#> A1 319.21 1060.38 NA NA NA</div><div class='input'>
<span class='co'># Using a single core, the following takes about 6 minutes as we do not have an</span>
<span class='co'># analytical solution. Using 10 cores it is slower instead of faster</span>
<span class='co'>#f_saem_fomc <- saem(f_mmkin["FOMC-SFO", ], cores = 1)</span>
<span class='co'># }</span>
</div></pre>
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