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for fixed effects (population), random effects (deviations from the
population mean) and residual error model, as well as the resulting
endpoints such as formation fractions and DT50 values. Optionally
(default is FALSE), the data are listed in full."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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<h6 class="dropdown-header" data-toc-skip>Example evaluations with hierarchical models (nonlinear mixed-effects models)</h6>
<a class="dropdown-item" href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
<a class="dropdown-item" href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a>
<a class="dropdown-item" href="../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a>
<a class="dropdown-item" href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a>
<a class="dropdown-item" href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a>
<a class="dropdown-item" href="../articles/web_only/multistart.html">Short demo of the multistart method</a>
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<a class="dropdown-item" href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
<a class="dropdown-item" href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
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<img src="" class="logo" alt=""><h1>Summary method for class "saem.mmkin"</h1>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/summary.saem.mmkin.R" class="external-link"><code>R/summary.saem.mmkin.R</code></a></small>
<div class="d-none name"><code>summary.saem.mmkin.Rd</code></div>
</div>
<div class="ref-description section level2">
<p>Lists model equations, initial parameter values, optimised parameters
for fixed effects (population), random effects (deviations from the
population mean) and residual error model, as well as the resulting
endpoints such as formation fractions and DT50 values. Optionally
(default is FALSE), the data are listed in full.</p>
</div>
<div class="section level2">
<h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
<div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for saem.mmkin</span></span>
<span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span></span>
<span> <span class="va">object</span>,</span>
<span> data <span class="op">=</span> <span class="cn">FALSE</span>,</span>
<span> verbose <span class="op">=</span> <span class="cn">FALSE</span>,</span>
<span> covariates <span class="op">=</span> <span class="cn">NULL</span>,</span>
<span> covariate_quantile <span class="op">=</span> <span class="fl">0.5</span>,</span>
<span> distimes <span class="op">=</span> <span class="cn">TRUE</span>,</span>
<span> <span class="va">...</span></span>
<span><span class="op">)</span></span>
<span></span>
<span><span class="co"># S3 method for summary.saem.mmkin</span></span>
<span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">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" class="external-link">max</a></span><span class="op">(</span><span class="fl">3</span>, <span class="fu"><a href="https://rdrr.io/r/base/options.html" class="external-link">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>, verbose <span class="op">=</span> <span class="va">x</span><span class="op">$</span><span class="va">verbose</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
</div>
<div class="section level2">
<h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
<dl><dt>object</dt>
<dd><p>an object of class <a href="saem.html">saem.mmkin</a></p></dd>
<dt>data</dt>
<dd><p>logical, indicating whether the full data should be included in
the summary.</p></dd>
<dt>verbose</dt>
<dd><p>Should the summary be verbose?</p></dd>
<dt>covariates</dt>
<dd><p>Numeric vector with covariate values for all variables in
any covariate models in the object. If given, it overrides 'covariate_quantile'.</p></dd>
<dt>covariate_quantile</dt>
<dd><p>This argument only has an effect if the fitted
object has covariate models. If so, the default is to show endpoints
for the median of the covariate values (50th percentile).</p></dd>
<dt>distimes</dt>
<dd><p>logical, indicating whether DT50 and DT90 values should be
included.</p></dd>
<dt>...</dt>
<dd><p>optional arguments passed to methods like <code>print</code>.</p></dd>
<dt>x</dt>
<dd><p>an object of class summary.saem.mmkin</p></dd>
<dt>digits</dt>
<dd><p>Number of digits to use for printing</p></dd>
</dl></div>
<div class="section level2">
<h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
<p>The summary function returns a list based on the <a href="https://rdrr.io/pkg/saemix/man/SaemixObject-class.html" class="external-link">saemix::SaemixObject</a></p>
<p>obtained in the fit, with at least the following additional components</p>
<dl><dt>saemixversion, mkinversion, Rversion</dt>
<dd><p>The saemix, mkin and R versions used</p></dd>
<dt>date.fit, date.summary</dt>
<dd><p>The dates where the fit and the summary were
produced</p></dd>
<dt>diffs</dt>
<dd><p>The differential equations used in the degradation model</p></dd>
<dt>use_of_ff</dt>
<dd><p>Was maximum or minimum use made of formation fractions</p></dd>
<dt>data</dt>
<dd><p>The data</p></dd>
<dt>confint_trans</dt>
<dd><p>Transformed parameters as used in the optimisation, with confidence intervals</p></dd>
<dt>confint_back</dt>
<dd><p>Backtransformed parameters, with confidence intervals if available</p></dd>
<dt>confint_errmod</dt>
<dd><p>Error model parameters with confidence intervals</p></dd>
<dt>ff</dt>
<dd><p>The estimated formation fractions derived from the fitted
model.</p></dd>
<dt>distimes</dt>
<dd><p>The DT50 and DT90 values for each observed variable.</p></dd>
<dt>SFORB</dt>
<dd><p>If applicable, eigenvalues of SFORB components of the model.</p></dd>
</dl><p>The print method is called for its side effect, i.e. printing the summary.</p>
</div>
<div class="section level2">
<h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
<p>Johannes Ranke for the mkin specific parts
saemix authors for the parts inherited from saemix.</p>
</div>
<div class="section level2">
<h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
<div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># Generate five datasets following DFOP-SFO kinetics</span></span></span>
<span class="r-in"><span><span class="va">sampling_times</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">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="fl">60</span>, <span class="fl">90</span>, <span class="fl">120</span><span class="op">)</span></span></span>
<span class="r-in"><span><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="mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="st">"m1"</span><span class="op">)</span>,</span></span>
<span class="r-in"><span> m1 <span class="op">=</span> <span class="fu"><a href="mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">1234</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">k1_in</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/Lognormal.html" class="external-link">rlnorm</a></span><span class="op">(</span><span class="fl">5</span>, <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.1</span><span class="op">)</span>, <span class="fl">0.3</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">k2_in</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/Lognormal.html" class="external-link">rlnorm</a></span><span class="op">(</span><span class="fl">5</span>, <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.02</span><span class="op">)</span>, <span class="fl">0.3</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">g_in</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/Logistic.html" class="external-link">plogis</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/Normal.html" class="external-link">rnorm</a></span><span class="op">(</span><span class="fl">5</span>, <span class="fu"><a href="https://rdrr.io/r/stats/Logistic.html" class="external-link">qlogis</a></span><span class="op">(</span><span class="fl">0.5</span><span class="op">)</span>, <span class="fl">0.3</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">f_parent_to_m1_in</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/Logistic.html" class="external-link">plogis</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/Normal.html" class="external-link">rnorm</a></span><span class="op">(</span><span class="fl">5</span>, <span class="fu"><a href="https://rdrr.io/r/stats/Logistic.html" class="external-link">qlogis</a></span><span class="op">(</span><span class="fl">0.3</span><span class="op">)</span>, <span class="fl">0.3</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">k_m1_in</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/Lognormal.html" class="external-link">rlnorm</a></span><span class="op">(</span><span class="fl">5</span>, <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">0.02</span><span class="op">)</span>, <span class="fl">0.3</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="va">pred_dfop_sfo</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">k1</span>, <span class="va">k2</span>, <span class="va">g</span>, <span class="va">f_parent_to_m1</span>, <span class="va">k_m1</span><span class="op">)</span> <span class="op">{</span></span></span>
<span class="r-in"><span> <span class="fu"><a href="mkinpredict.html">mkinpredict</a></span><span class="op">(</span><span class="va">dfop_sfo</span>,</span></span>
<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>k1 <span class="op">=</span> <span class="va">k1</span>, k2 <span class="op">=</span> <span class="va">k2</span>, g <span class="op">=</span> <span class="va">g</span>, f_parent_to_m1 <span class="op">=</span> <span class="va">f_parent_to_m1</span>, k_m1 <span class="op">=</span> <span class="va">k_m1</span><span class="op">)</span>,</span></span>
<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fl">100</span>, m1 <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>,</span></span>
<span class="r-in"><span> <span class="va">sampling_times</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="op">}</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="va">ds_mean_dfop_sfo</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">5</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span></span>
<span class="r-in"><span> <span class="fu"><a href="mkinpredict.html">mkinpredict</a></span><span class="op">(</span><span class="va">dfop_sfo</span>,</span></span>
<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>k1 <span class="op">=</span> <span class="va">k1_in</span><span class="op">[</span><span class="va">i</span><span class="op">]</span>, k2 <span class="op">=</span> <span class="va">k2_in</span><span class="op">[</span><span class="va">i</span><span class="op">]</span>, g <span class="op">=</span> <span class="va">g_in</span><span class="op">[</span><span class="va">i</span><span class="op">]</span>,</span></span>
<span class="r-in"><span> f_parent_to_m1 <span class="op">=</span> <span class="va">f_parent_to_m1_in</span><span class="op">[</span><span class="va">i</span><span class="op">]</span>, k_m1 <span class="op">=</span> <span class="va">k_m1_in</span><span class="op">[</span><span class="va">i</span><span class="op">]</span><span class="op">)</span>,</span></span>
<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fl">100</span>, m1 <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>,</span></span>
<span class="r-in"><span> <span class="va">sampling_times</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="op">}</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">ds_mean_dfop_sfo</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"ds"</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">5</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="va">ds_syn_dfop_sfo</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="va">ds_mean_dfop_sfo</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="op">{</span></span></span>
<span class="r-in"><span> <span class="fu"><a href="add_err.html">add_err</a></span><span class="op">(</span><span class="va">ds</span>,</span></span>
<span class="r-in"><span> sdfunc <span class="op">=</span> <span class="kw">function</span><span class="op">(</span><span class="va">value</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="fl">1</span><span class="op">^</span><span class="fl">2</span> <span class="op">+</span> <span class="va">value</span><span class="op">^</span><span class="fl">2</span> <span class="op">*</span> <span class="fl">0.07</span><span class="op">^</span><span class="fl">2</span><span class="op">)</span>,</span></span>
<span class="r-in"><span> n <span class="op">=</span> <span class="fl">1</span><span class="op">)</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span></span></span>
<span class="r-in"><span><span class="op">}</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
<span class="r-in"><span><span class="co"># Evaluate using mmkin and saem</span></span></span>
<span class="r-in"><span><span class="va">f_mmkin_dfop_sfo</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" class="external-link">list</a></span><span class="op">(</span><span class="va">dfop_sfo</span><span class="op">)</span>, <span class="va">ds_syn_dfop_sfo</span>,</span></span>
<span class="r-in"><span> quiet <span class="op">=</span> <span class="cn">TRUE</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>, cores <span class="op">=</span> <span class="fl">5</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">f_saem_dfop_sfo</span> <span class="op"><-</span> <span class="fu"><a href="saem.html">saem</a></span><span class="op">(</span><span class="va">f_mmkin_dfop_sfo</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">f_saem_dfop_sfo</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Kinetic nonlinear mixed-effects model fit by SAEM</span>
<span class="r-out co"><span class="r-pr">#></span> Structural model:</span>
<span class="r-out co"><span class="r-pr">#></span> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span>
<span class="r-out co"><span class="r-pr">#></span> time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))</span>
<span class="r-out co"><span class="r-pr">#></span> * parent</span>
<span class="r-out co"><span class="r-pr">#></span> d_m1/dt = + f_parent_to_m1 * ((k1 * g * exp(-k1 * time) + k2 * (1 - g)</span>
<span class="r-out co"><span class="r-pr">#></span> * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *</span>
<span class="r-out co"><span class="r-pr">#></span> exp(-k2 * time))) * parent - k_m1 * m1</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Data:</span>
<span class="r-out co"><span class="r-pr">#></span> 171 observations of 2 variable(s) grouped in 5 datasets</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Likelihood computed by importance sampling</span>
<span class="r-out co"><span class="r-pr">#></span> AIC BIC logLik</span>
<span class="r-out co"><span class="r-pr">#></span> 810.8 805.4 -391.4</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Fitted parameters:</span>
<span class="r-out co"><span class="r-pr">#></span> estimate lower upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 100.966822 97.90584 104.0278</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_m1 -4.076164 -4.17485 -3.9775</span>
<span class="r-out co"><span class="r-pr">#></span> f_parent_qlogis -0.940902 -1.35358 -0.5282</span>
<span class="r-out co"><span class="r-pr">#></span> log_k1 -2.363988 -2.71690 -2.0111</span>
<span class="r-out co"><span class="r-pr">#></span> log_k2 -4.060016 -4.21743 -3.9026</span>
<span class="r-out co"><span class="r-pr">#></span> g_qlogis -0.029999 -0.44766 0.3877</span>
<span class="r-out co"><span class="r-pr">#></span> a.1 0.876272 0.67308 1.0795</span>
<span class="r-out co"><span class="r-pr">#></span> b.1 0.079594 0.06399 0.0952</span>
<span class="r-out co"><span class="r-pr">#></span> SD.parent_0 0.076322 -76.47330 76.6259</span>
<span class="r-out co"><span class="r-pr">#></span> SD.log_k_m1 0.005052 -1.09071 1.1008</span>
<span class="r-out co"><span class="r-pr">#></span> SD.f_parent_qlogis 0.446968 0.16577 0.7282</span>
<span class="r-out co"><span class="r-pr">#></span> SD.log_k1 0.348786 0.09502 0.6025</span>
<span class="r-out co"><span class="r-pr">#></span> SD.log_k2 0.147456 0.03111 0.2638</span>
<span class="r-out co"><span class="r-pr">#></span> SD.g_qlogis 0.348244 0.02794 0.6686</span>
<span class="r-in"><span><span class="fu"><a href="illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_dfop_sfo</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] "sd(parent_0)" "sd(log_k_m1)"</span>
<span class="r-in"><span><span class="va">f_saem_dfop_sfo_2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_dfop_sfo</span>,</span></span>
<span class="r-in"><span> no_random_effect <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"parent_0"</span>, <span class="st">"log_k_m1"</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="fu"><a href="illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_dfop_sfo_2</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/intervals.html" class="external-link">intervals</a></span><span class="op">(</span><span class="va">f_saem_dfop_sfo_2</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Approximate 95% confidence intervals</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Fixed effects:</span>
<span class="r-out co"><span class="r-pr">#></span> lower est. upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 98.04247057 101.09950884 104.15654711</span>
<span class="r-out co"><span class="r-pr">#></span> k_m1 0.01528983 0.01687734 0.01862969</span>
<span class="r-out co"><span class="r-pr">#></span> f_parent_to_m1 0.20447650 0.27932896 0.36887691</span>
<span class="r-out co"><span class="r-pr">#></span> k1 0.06779844 0.09638524 0.13702550</span>
<span class="r-out co"><span class="r-pr">#></span> k2 0.01495629 0.01741775 0.02028431</span>
<span class="r-out co"><span class="r-pr">#></span> g 0.37669311 0.48368409 0.59219202</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Random effects:</span>
<span class="r-out co"><span class="r-pr">#></span> lower est. upper</span>
<span class="r-out co"><span class="r-pr">#></span> sd(f_parent_qlogis) 0.16515100 0.4448330 0.7245149</span>
<span class="r-out co"><span class="r-pr">#></span> sd(log_k1) 0.08982372 0.3447403 0.5996568</span>
<span class="r-out co"><span class="r-pr">#></span> sd(log_k2) 0.02806589 0.1419560 0.2558462</span>
<span class="r-out co"><span class="r-pr">#></span> sd(g_qlogis) 0.04908160 0.3801993 0.7113170</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> lower est. upper</span>
<span class="r-out co"><span class="r-pr">#></span> a.1 0.67539922 0.87630147 1.07720371</span>
<span class="r-out co"><span class="r-pr">#></span> b.1 0.06401324 0.07920531 0.09439739</span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">f_saem_dfop_sfo_2</span>, data <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> saemix version used for fitting: 3.2 </span>
<span class="r-out co"><span class="r-pr">#></span> mkin version used for pre-fitting: 1.2.6 </span>
<span class="r-out co"><span class="r-pr">#></span> R version used for fitting: 4.3.2 </span>
<span class="r-out co"><span class="r-pr">#></span> Date of fit: Thu Nov 16 04:19:57 2023 </span>
<span class="r-out co"><span class="r-pr">#></span> Date of summary: Thu Nov 16 04:19:57 2023 </span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Equations:</span>
<span class="r-out co"><span class="r-pr">#></span> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *</span>
<span class="r-out co"><span class="r-pr">#></span> time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))</span>
<span class="r-out co"><span class="r-pr">#></span> * parent</span>
<span class="r-out co"><span class="r-pr">#></span> d_m1/dt = + f_parent_to_m1 * ((k1 * g * exp(-k1 * time) + k2 * (1 - g)</span>
<span class="r-out co"><span class="r-pr">#></span> * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *</span>
<span class="r-out co"><span class="r-pr">#></span> exp(-k2 * time))) * parent - k_m1 * m1</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Data:</span>
<span class="r-out co"><span class="r-pr">#></span> 171 observations of 2 variable(s) grouped in 5 datasets</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Model predictions using solution type analytical </span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Fitted in 9.193 s</span>
<span class="r-out co"><span class="r-pr">#></span> Using 300, 100 iterations and 10 chains</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Variance model: Two-component variance function </span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Starting values for degradation parameters:</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 log_k_m1 f_parent_qlogis log_k1 log_k2 </span>
<span class="r-out co"><span class="r-pr">#></span> 101.65645 -4.05368 -0.94311 -2.35943 -4.07006 </span>
<span class="r-out co"><span class="r-pr">#></span> g_qlogis </span>
<span class="r-out co"><span class="r-pr">#></span> -0.01133 </span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Fixed degradation parameter values:</span>
<span class="r-out co"><span class="r-pr">#></span> None</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Starting values for random effects (square root of initial entries in omega):</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 log_k_m1 f_parent_qlogis log_k1 log_k2 g_qlogis</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 6.742 0.0000 0.0000 0.0000 0.0000 0.000</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_m1 0.000 0.2236 0.0000 0.0000 0.0000 0.000</span>
<span class="r-out co"><span class="r-pr">#></span> f_parent_qlogis 0.000 0.0000 0.5572 0.0000 0.0000 0.000</span>
<span class="r-out co"><span class="r-pr">#></span> log_k1 0.000 0.0000 0.0000 0.8031 0.0000 0.000</span>
<span class="r-out co"><span class="r-pr">#></span> log_k2 0.000 0.0000 0.0000 0.0000 0.2931 0.000</span>
<span class="r-out co"><span class="r-pr">#></span> g_qlogis 0.000 0.0000 0.0000 0.0000 0.0000 0.807</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Starting values for error model parameters:</span>
<span class="r-out co"><span class="r-pr">#></span> a.1 b.1 </span>
<span class="r-out co"><span class="r-pr">#></span> 1 1 </span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Results:</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Likelihood computed by importance sampling</span>
<span class="r-out co"><span class="r-pr">#></span> AIC BIC logLik</span>
<span class="r-out co"><span class="r-pr">#></span> 806.9 802.2 -391.5</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Optimised parameters:</span>
<span class="r-out co"><span class="r-pr">#></span> est. lower upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 101.09951 98.04247 104.1565</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_m1 -4.08178 -4.18057 -3.9830</span>
<span class="r-out co"><span class="r-pr">#></span> f_parent_qlogis -0.94779 -1.35855 -0.5370</span>
<span class="r-out co"><span class="r-pr">#></span> log_k1 -2.33940 -2.69122 -1.9876</span>
<span class="r-out co"><span class="r-pr">#></span> log_k2 -4.05027 -4.20262 -3.8979</span>
<span class="r-out co"><span class="r-pr">#></span> g_qlogis -0.06529 -0.50361 0.3730</span>
<span class="r-out co"><span class="r-pr">#></span> a.1 0.87630 0.67540 1.0772</span>
<span class="r-out co"><span class="r-pr">#></span> b.1 0.07921 0.06401 0.0944</span>
<span class="r-out co"><span class="r-pr">#></span> SD.f_parent_qlogis 0.44483 0.16515 0.7245</span>
<span class="r-out co"><span class="r-pr">#></span> SD.log_k1 0.34474 0.08982 0.5997</span>
<span class="r-out co"><span class="r-pr">#></span> SD.log_k2 0.14196 0.02807 0.2558</span>
<span class="r-out co"><span class="r-pr">#></span> SD.g_qlogis 0.38020 0.04908 0.7113</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Correlation: </span>
<span class="r-out co"><span class="r-pr">#></span> parnt_0 lg_k_m1 f_prnt_ log_k1 log_k2 </span>
<span class="r-out co"><span class="r-pr">#></span> log_k_m1 -0.4716 </span>
<span class="r-out co"><span class="r-pr">#></span> f_parent_qlogis -0.2394 0.2617 </span>
<span class="r-out co"><span class="r-pr">#></span> log_k1 0.1677 -0.1566 -0.0659 </span>
<span class="r-out co"><span class="r-pr">#></span> log_k2 0.0165 0.0638 0.0045 0.2013 </span>
<span class="r-out co"><span class="r-pr">#></span> g_qlogis 0.1118 -0.1118 -0.0340 -0.2324 -0.3419</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Random effects:</span>
<span class="r-out co"><span class="r-pr">#></span> est. lower upper</span>
<span class="r-out co"><span class="r-pr">#></span> SD.f_parent_qlogis 0.4448 0.16515 0.7245</span>
<span class="r-out co"><span class="r-pr">#></span> SD.log_k1 0.3447 0.08982 0.5997</span>
<span class="r-out co"><span class="r-pr">#></span> SD.log_k2 0.1420 0.02807 0.2558</span>
<span class="r-out co"><span class="r-pr">#></span> SD.g_qlogis 0.3802 0.04908 0.7113</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Variance model:</span>
<span class="r-out co"><span class="r-pr">#></span> est. lower upper</span>
<span class="r-out co"><span class="r-pr">#></span> a.1 0.87630 0.67540 1.0772</span>
<span class="r-out co"><span class="r-pr">#></span> b.1 0.07921 0.06401 0.0944</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Backtransformed parameters:</span>
<span class="r-out co"><span class="r-pr">#></span> est. lower upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 101.09951 98.04247 104.15655</span>
<span class="r-out co"><span class="r-pr">#></span> k_m1 0.01688 0.01529 0.01863</span>
<span class="r-out co"><span class="r-pr">#></span> f_parent_to_m1 0.27933 0.20448 0.36888</span>
<span class="r-out co"><span class="r-pr">#></span> k1 0.09639 0.06780 0.13703</span>
<span class="r-out co"><span class="r-pr">#></span> k2 0.01742 0.01496 0.02028</span>
<span class="r-out co"><span class="r-pr">#></span> g 0.48368 0.37669 0.59219</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Resulting formation fractions:</span>
<span class="r-out co"><span class="r-pr">#></span> ff</span>
<span class="r-out co"><span class="r-pr">#></span> parent_m1 0.2793</span>
<span class="r-out co"><span class="r-pr">#></span> parent_sink 0.7207</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Estimated disappearance times:</span>
<span class="r-out co"><span class="r-pr">#></span> DT50 DT90 DT50back DT50_k1 DT50_k2</span>
<span class="r-out co"><span class="r-pr">#></span> parent 15.66 94.28 28.38 7.191 39.8</span>
<span class="r-out co"><span class="r-pr">#></span> m1 41.07 136.43 NA NA NA</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Data:</span>
<span class="r-out co"><span class="r-pr">#></span> ds name time observed predicted residual std standardized</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 0 89.8 1.011e+02 -11.29951 8.0554 -1.402721</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 0 104.1 1.011e+02 3.00049 8.0554 0.372481</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 1 88.7 9.624e+01 -7.53600 7.6726 -0.982195</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 1 95.5 9.624e+01 -0.73600 7.6726 -0.095925</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 3 81.8 8.736e+01 -5.55672 6.9744 -0.796732</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 3 94.5 8.736e+01 7.14328 6.9744 1.024217</span>
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<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 3 7.5 8.448e+00 -0.94789 1.1026 -0.859720</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 7 16.5 1.581e+01 0.68760 1.5286 0.449839</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 7 19.0 1.581e+01 3.18760 1.5286 2.085373</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 14 22.9 2.218e+01 0.71983 1.9632 0.366658</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 14 23.2 2.218e+01 1.01983 1.9632 0.519469</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 28 22.2 2.425e+01 -2.05105 2.1113 -0.971479</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 28 24.4 2.425e+01 0.14895 2.1113 0.070552</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 60 15.5 1.876e+01 -3.25968 1.7250 -1.889646</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 60 19.8 1.876e+01 1.04032 1.7250 0.603074</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 90 14.9 1.365e+01 1.25477 1.3914 0.901806</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 90 14.2 1.365e+01 0.55477 1.3914 0.398714</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 120 10.9 9.726e+00 1.17443 1.1667 1.006587</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 m1 120 10.4 9.726e+00 0.67443 1.1667 0.578044</span>
<span class="r-in"><span><span class="co"># Add a correlation between random effects of g and k2</span></span></span>
<span class="r-in"><span><span class="va">cov_model_3</span> <span class="op"><-</span> <span class="va">f_saem_dfop_sfo_2</span><span class="op">$</span><span class="va">so</span><span class="op">@</span><span class="va">model</span><span class="op">@</span><span class="va">covariance.model</span></span></span>
<span class="r-in"><span><span class="va">cov_model_3</span><span class="op">[</span><span class="st">"log_k2"</span>, <span class="st">"g_qlogis"</span><span class="op">]</span> <span class="op"><-</span> <span class="fl">1</span></span></span>
<span class="r-in"><span><span class="va">cov_model_3</span><span class="op">[</span><span class="st">"g_qlogis"</span>, <span class="st">"log_k2"</span><span class="op">]</span> <span class="op"><-</span> <span class="fl">1</span></span></span>
<span class="r-in"><span><span class="va">f_saem_dfop_sfo_3</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_dfop_sfo</span>,</span></span>
<span class="r-in"><span> covariance.model <span class="op">=</span> <span class="va">cov_model_3</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/pkg/nlme/man/intervals.html" class="external-link">intervals</a></span><span class="op">(</span><span class="va">f_saem_dfop_sfo_3</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Approximate 95% confidence intervals</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Fixed effects:</span>
<span class="r-out co"><span class="r-pr">#></span> lower est. upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 98.42519529 101.51623115 104.60726702</span>
<span class="r-out co"><span class="r-pr">#></span> k_m1 0.01505059 0.01662123 0.01835577</span>
<span class="r-out co"><span class="r-pr">#></span> f_parent_to_m1 0.20100222 0.27477835 0.36332008</span>
<span class="r-out co"><span class="r-pr">#></span> k1 0.07347479 0.10139028 0.13991179</span>
<span class="r-out co"><span class="r-pr">#></span> k2 0.01469861 0.01771120 0.02134125</span>
<span class="r-out co"><span class="r-pr">#></span> g 0.35506898 0.46263682 0.57379888</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Random effects:</span>
<span class="r-out co"><span class="r-pr">#></span> lower est. upper</span>
<span class="r-out co"><span class="r-pr">#></span> sd(f_parent_qlogis) 0.3827416 0.4435866 0.5044315</span>
<span class="r-out co"><span class="r-pr">#></span> sd(log_k1) 0.1226277 0.2981783 0.4737289</span>
<span class="r-out co"><span class="r-pr">#></span> sd(log_k2) -0.5457764 0.1912531 0.9282825</span>
<span class="r-out co"><span class="r-pr">#></span> sd(g_qlogis) 0.1483976 0.3997298 0.6510619</span>
<span class="r-out co"><span class="r-pr">#></span> corr(log_k2,g_qlogis) -0.8537145 -0.5845703 -0.3154261</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> lower est. upper</span>
<span class="r-out co"><span class="r-pr">#></span> a.1 0.6732869 0.87421677 1.0751467</span>
<span class="r-out co"><span class="r-pr">#></span> b.1 0.0640392 0.07925135 0.0944635</span>
<span class="r-in"><span><span class="co"># The correlation does not improve the fit judged by AIC and BIC, although</span></span></span>
<span class="r-in"><span><span class="co"># the likelihood is higher with the additional parameter</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_dfop_sfo</span>, <span class="va">f_saem_dfop_sfo_2</span>, <span class="va">f_saem_dfop_sfo_3</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Data: 171 observations of 2 variable(s) grouped in 5 datasets</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> npar AIC BIC Lik</span>
<span class="r-out co"><span class="r-pr">#></span> f_saem_dfop_sfo_2 12 806.91 802.23 -391.46</span>
<span class="r-out co"><span class="r-pr">#></span> f_saem_dfop_sfo_3 13 807.96 802.88 -390.98</span>
<span class="r-out co"><span class="r-pr">#></span> f_saem_dfop_sfo 14 810.83 805.36 -391.41</span>
<span class="r-in"><span><span class="co"># }</span></span></span>
<span class="r-in"><span></span></span>
</code></pre></div>
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