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<!DOCTYPE html>
<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Summary method for class "nlme.mmkin" — summary.nlme.mmkin • mkin</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Summary method for class " nlme.mmkin summary.nlme.mmkin><meta property="og:description" content="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."><!-- 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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<h1>Summary method for class "nlme.mmkin"</h1>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/summary.nlme.mmkin.R" class="external-link"><code>R/summary.nlme.mmkin.R</code></a></small>
<div class="hidden name"><code>summary.nlme.mmkin.Rd</code></div>
</div>
<div class="ref-description">
<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 id="ref-usage">
<div class="sourceCode"><pre class="sourceCode r"><code><span class="co"># S3 method for nlme.mmkin</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">object</span>,
data <span class="op">=</span> <span class="cn">FALSE</span>,
verbose <span class="op">=</span> <span class="cn">FALSE</span>,
distimes <span class="op">=</span> <span class="cn">TRUE</span>,
alpha <span class="op">=</span> <span class="fl">0.05</span>,
<span class="va">...</span>
<span class="op">)</span>
<span class="co"># S3 method for summary.nlme.mmkin</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></code></pre></div>
</div>
<div id="arguments">
<h2>Arguments</h2>
<dl><dt>object</dt>
<dd><p>an object of class <a href="nlme.mmkin.html">nlme.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>distimes</dt>
<dd><p>logical, indicating whether DT50 and DT90 values should be
included.</p></dd>
<dt>alpha</dt>
<dd><p>error level for confidence interval estimation from the t
distribution</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.nlme.mmkin</p></dd>
<dt>digits</dt>
<dd><p>Number of digits to use for printing</p></dd>
</dl></div>
<div id="value">
<h2>Value</h2>
<p>The summary function returns a list based on the <a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a> object
obtained in the fit, with at least the following additional components</p>
<dl><dt>nlmeversion, mkinversion, Rversion</dt>
<dd><p>The nlme, 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>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 id="author">
<h2>Author</h2>
<p>Johannes Ranke for the mkin specific parts
José Pinheiro and Douglas Bates for the components inherited from nlme</p>
</div>
<div id="ref-examples">
<h2>Examples</h2>
<div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"></span>
<span class="r-in"><span class="co"># Generate five datasets following SFO kinetics</span></span>
<span class="r-in"><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 class="r-in"><span class="va">dt50_sfo_in_pop</span> <span class="op"><-</span> <span class="fl">50</span></span>
<span class="r-in"><span class="va">k_in_pop</span> <span class="op"><-</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">2</span><span class="op">)</span> <span class="op">/</span> <span class="va">dt50_sfo_in_pop</span></span>
<span class="r-in"><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 class="r-in"><span class="va">k_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="va">k_in_pop</span><span class="op">)</span>, <span class="fl">0.5</span><span class="op">)</span></span>
<span class="r-in"><span class="va">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">"SFO"</span><span class="op">)</span><span class="op">)</span></span>
<span class="r-in"></span>
<span class="r-in"><span class="va">pred_sfo</span> <span class="op"><-</span> <span class="kw">function</span><span class="op">(</span><span class="va">k</span><span class="op">)</span> <span class="op">{</span></span>
<span class="r-in"> <span class="fu"><a href="mkinpredict.html">mkinpredict</a></span><span class="op">(</span><span class="va">SFO</span>,</span>
<span class="r-in"> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>k_parent <span class="op">=</span> <span class="va">k</span><span class="op">)</span>,</span>
<span class="r-in"> <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><span class="op">)</span>,</span>
<span class="r-in"> <span class="va">sampling_times</span><span class="op">)</span></span>
<span class="r-in"><span class="op">}</span></span>
<span class="r-in"></span>
<span class="r-in"><span class="va">ds_sfo_mean</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">k_in</span>, <span class="va">pred_sfo</span><span class="op">)</span></span>
<span class="r-in"><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_sfo_mean</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 class="r-in"></span>
<span class="r-in"><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">12345</span><span class="op">)</span></span>
<span class="r-in"><span class="va">ds_sfo_syn</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_sfo_mean</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 class="r-in"> <span class="fu"><a href="add_err.html">add_err</a></span><span class="op">(</span><span class="va">ds</span>,</span>
<span class="r-in"> 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 class="r-in"> 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 class="r-in"><span class="op">}</span><span class="op">)</span></span>
<span class="r-in"></span>
<span class="r-in"><span class="co"># \dontrun{</span></span>
<span class="r-in"><span class="co"># Evaluate using mmkin and nlme</span></span>
<span class="r-in"><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://svn.r-project.org/R-packages/trunk/nlme/" class="external-link">nlme</a></span><span class="op">)</span></span>
<span class="r-in"><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="st">"SFO"</span>, <span class="va">ds_sfo_syn</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">1</span><span class="op">)</span></span>
<span class="r-in"><span class="va">f_nlme</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/nlme.html" class="external-link">nlme</a></span><span class="op">(</span><span class="va">f_mmkin</span><span class="op">)</span></span>
<span class="r-wrn co"><span class="r-pr">#></span> <span class="warning">Warning: </span>Iteration 4, LME step: nlminb() did not converge (code = 1). PORT message: false convergence (8)</span>
<span class="r-in"><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_nlme</span>, data <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
<span class="r-out co"><span class="r-pr">#></span> nlme version used for fitting: 3.1.155 </span>
<span class="r-out co"><span class="r-pr">#></span> mkin version used for pre-fitting: 1.1.0 </span>
<span class="r-out co"><span class="r-pr">#></span> R version used for fitting: 4.2.1 </span>
<span class="r-out co"><span class="r-pr">#></span> Date of fit: Thu Jun 30 10:23:57 2022 </span>
<span class="r-out co"><span class="r-pr">#></span> Date of summary: Thu Jun 30 10:23:57 2022 </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 = - k_parent * parent</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> 90 observations of 1 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 0.538 s using 4 iterations</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> Mean of starting values for individual parameters:</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 log_k_parent </span>
<span class="r-out co"><span class="r-pr">#></span> 101.612 -4.454 </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> Results:</span>
<span class="r-out co"><span class="r-pr">#></span> </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> 584.5 599.5 -286.2</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Optimised, transformed parameters with symmetric confidence intervals:</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 99.371 101.592 103.814</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_parent -4.973 -4.449 -3.926</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</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_parent 0.0507 </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> Formula: list(parent_0 ~ 1, log_k_parent ~ 1)</span>
<span class="r-out co"><span class="r-pr">#></span> Level: ds</span>
<span class="r-out co"><span class="r-pr">#></span> Structure: Diagonal</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 log_k_parent Residual</span>
<span class="r-out co"><span class="r-pr">#></span> StdDev: 6.904e-05 0.5863 1</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Variance function:</span>
<span class="r-out co"><span class="r-pr">#></span> Structure: Constant plus proportion of variance covariate</span>
<span class="r-out co"><span class="r-pr">#></span> Formula: ~fitted(.) </span>
<span class="r-out co"><span class="r-pr">#></span> Parameter estimates:</span>
<span class="r-out co"><span class="r-pr">#></span> const prop </span>
<span class="r-out co"><span class="r-pr">#></span> 0.000121099 0.078996777 </span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Backtransformed parameters with asymmetric confidence intervals:</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 99.370886 101.59243 103.81398</span>
<span class="r-out co"><span class="r-pr">#></span> k_parent 0.006923 0.01168 0.01972</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</span>
<span class="r-out co"><span class="r-pr">#></span> parent 59.32 197.1</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 0 104.1 101.592 2.50757 8.0255 0.312451</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 0 105.0 101.592 3.40757 8.0255 0.424594</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 1 98.5 100.796 -2.29571 7.9625 -0.288314</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 1 96.1 100.796 -4.69571 7.9625 -0.589725</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 3 101.9 99.221 2.67904 7.8381 0.341796</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 3 85.2 99.221 -14.02096 7.8381 -1.788813</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 7 99.1 96.145 2.95512 7.5951 0.389080</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 7 93.0 96.145 -3.14488 7.5951 -0.414065</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 14 88.1 90.989 -2.88944 7.1879 -0.401988</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 14 84.1 90.989 -6.88944 7.1879 -0.958481</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 28 80.2 81.493 -1.29305 6.4377 -0.200857</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 28 91.3 81.493 9.80695 6.4377 1.523364</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 60 65.1 63.344 1.75642 5.0039 0.351008</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 60 65.8 63.344 2.45642 5.0039 0.490898</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 90 47.8 50.018 -2.21764 3.9512 -0.561253</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 90 53.5 50.018 3.48236 3.9512 0.881335</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 120 37.6 39.495 -1.89515 3.1200 -0.607423</span>
<span class="r-out co"><span class="r-pr">#></span> ds 1 parent 120 39.3 39.495 -0.19515 3.1200 -0.062549</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 0 107.9 101.592 6.30757 8.0255 0.785943</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 0 102.1 101.592 0.50757 8.0255 0.063244</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 1 103.8 100.058 3.74159 7.9043 0.473361</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 1 108.6 100.058 8.54159 7.9043 1.080626</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 3 91.0 97.060 -6.05952 7.6674 -0.790297</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 3 84.9 97.060 -12.15952 7.6674 -1.585875</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 7 79.3 91.329 -12.02867 7.2147 -1.667252</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 7 100.9 91.329 9.57133 7.2147 1.326647</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 14 77.3 82.102 -4.80185 6.4858 -0.740366</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 14 83.5 82.102 1.39815 6.4858 0.215571</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 28 66.8 66.351 0.44945 5.2415 0.085748</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 28 63.3 66.351 -3.05055 5.2415 -0.582002</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 60 40.8 40.775 0.02474 3.2211 0.007681</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 60 44.8 40.775 4.02474 3.2211 1.249487</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 90 27.8 25.832 1.96762 2.0407 0.964200</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 90 27.0 25.832 1.16762 2.0407 0.572173</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 120 15.2 16.366 -1.16561 1.2928 -0.901593</span>
<span class="r-out co"><span class="r-pr">#></span> ds 2 parent 120 15.5 16.366 -0.86561 1.2928 -0.669544</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 0 97.7 101.592 -3.89243 8.0255 -0.485010</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 0 88.2 101.592 -13.39243 8.0255 -1.668740</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 1 109.9 99.218 10.68195 7.8379 1.362858</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 1 97.8 99.218 -1.41805 7.8379 -0.180921</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 3 100.5 94.634 5.86555 7.4758 0.784603</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 3 77.4 94.634 -17.23445 7.4758 -2.305361</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 7 78.3 86.093 -7.79273 6.8010 -1.145814</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 7 90.3 86.093 4.20727 6.8010 0.618620</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 14 76.0 72.958 3.04222 5.7634 0.527848</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 14 79.1 72.958 6.14222 5.7634 1.065722</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 28 46.0 52.394 -6.39404 4.1390 -1.544842</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 28 53.4 52.394 1.00596 4.1390 0.243046</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 60 25.1 24.582 0.51786 1.9419 0.266676</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 60 21.4 24.582 -3.18214 1.9419 -1.638664</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 90 11.0 12.092 -1.09202 0.9552 -1.143199</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 90 14.2 12.092 2.10798 0.9552 2.206778</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 120 5.8 5.948 -0.14810 0.4699 -0.315178</span>
<span class="r-out co"><span class="r-pr">#></span> ds 3 parent 120 6.1 5.948 0.15190 0.4699 0.323283</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 0 95.3 101.592 -6.29243 8.0255 -0.784057</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 0 102.0 101.592 0.40757 8.0255 0.050784</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 1 104.4 101.125 3.27549 7.9885 0.410025</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 1 105.4 101.125 4.27549 7.9885 0.535204</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 3 113.7 100.195 13.50487 7.9151 1.706218</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 3 82.3 100.195 -17.89513 7.9151 -2.260887</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 7 98.1 98.362 -0.26191 7.7703 -0.033706</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 7 87.8 98.362 -10.56191 7.7703 -1.359271</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 14 97.9 95.234 2.66589 7.5232 0.354356</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 14 104.8 95.234 9.56589 7.5232 1.271521</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 28 85.0 89.274 -4.27373 7.0523 -0.606002</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 28 77.2 89.274 -12.07373 7.0523 -1.712019</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 60 82.2 77.013 5.18659 6.0838 0.852523</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 60 86.1 77.013 9.08659 6.0838 1.493568</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 90 70.5 67.053 3.44690 5.2970 0.650729</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 90 61.7 67.053 -5.35310 5.2970 -1.010595</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 120 60.0 58.381 1.61902 4.6119 0.351052</span>
<span class="r-out co"><span class="r-pr">#></span> ds 4 parent 120 56.4 58.381 -1.98098 4.6119 -0.429535</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 0 92.6 101.592 -8.99243 8.0255 -1.120486</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 0 116.5 101.592 14.90757 8.0255 1.857531</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 1 108.0 99.914 8.08560 7.8929 1.024412</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 1 104.9 99.914 4.98560 7.8929 0.631655</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 3 100.5 96.641 3.85898 7.6343 0.505477</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 3 89.5 96.641 -7.14102 7.6343 -0.935383</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 7 91.7 90.412 1.28752 7.1423 0.180267</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 7 95.1 90.412 4.68752 7.1423 0.656304</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 14 82.2 80.463 1.73715 6.3563 0.273296</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 14 84.5 80.463 4.03715 6.3563 0.635141</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 28 60.5 63.728 -3.22788 5.0343 -0.641178</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 28 72.8 63.728 9.07212 5.0343 1.802063</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 60 38.3 37.399 0.90062 2.9544 0.304836</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 60 40.7 37.399 3.30062 2.9544 1.117176</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 90 22.5 22.692 -0.19164 1.7926 -0.106910</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 90 20.8 22.692 -1.89164 1.7926 -1.055271</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 120 13.4 13.768 -0.36789 1.0876 -0.338255</span>
<span class="r-out co"><span class="r-pr">#></span> ds 5 parent 120 13.8 13.768 0.03211 1.0876 0.029520</span>
<span class="r-in"><span class="co"># }</span></span>
<span class="r-in"></span>
</code></pre></div>
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