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authorJohannes Ranke <jranke@uni-bremen.de>2021-02-03 16:41:31 +0100
committerJohannes Ranke <jranke@uni-bremen.de>2021-02-03 18:18:19 +0100
commitf0ef23a7598e5d19648ae4edc2b74e0fba27a41c (patch)
tree03af20e730330e148acf3a7c008d82387dbe52eb /docs/reference/summary.nlme.mmkin.html
parent82814b17ec182467c25325d747fffa8ffbe4bb33 (diff)
Prepare for v1.0.0v1.0.0
- Improve authorship and copyright information - Prepare pkgdown config - Remove dependence on saemix as we need the development version which is not ready for CRAN - Temporarily remove saemix interface to check code coverage of the rest
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+<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." />
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+ <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
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+ <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
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+ <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
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+ <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
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+ <div class="page-header">
+ <h1>Summary method for class "nlme.mmkin"</h1>
+ <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/summary.nlme.mmkin.R'><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>
+
+ <pre class="usage"><span class='co'># S3 method for nlme.mmkin</span>
+<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>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'>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>, 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></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 object of class <a href='nlme.mmkin.html'>nlme.mmkin</a></p></td>
+ </tr>
+ <tr>
+ <th>data</th>
+ <td><p>logical, indicating whether the full data should be included in
+the summary.</p></td>
+ </tr>
+ <tr>
+ <th>verbose</th>
+ <td><p>Should the summary be verbose?</p></td>
+ </tr>
+ <tr>
+ <th>distimes</th>
+ <td><p>logical, indicating whether DT50 and DT90 values should be
+included.</p></td>
+ </tr>
+ <tr>
+ <th>alpha</th>
+ <td><p>error level for confidence interval estimation from the t
+distribution</p></td>
+ </tr>
+ <tr>
+ <th>...</th>
+ <td><p>optional arguments passed to methods like <code>print</code>.</p></td>
+ </tr>
+ <tr>
+ <th>x</th>
+ <td><p>an object of class summary.nlme.mmkin</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>The summary function returns a list based on the <a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a> object
+obtained in the fit, with at least the following additional components</p>
+<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>
+The print method is called for its side effect, i.e. printing the summary.
+
+ <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+ <p>Johannes Ranke for the mkin specific parts
+José Pinheiro and Douglas Bates for the components inherited from nlme</p>
+
+ <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
+ <pre class="examples"><div class='input'>
+<span class='co'># Generate five datasets following SFO kinetics</span>
+<span class='va'>sampling_times</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='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 class='va'>dt50_sfo_in_pop</span> <span class='op'>&lt;-</span> <span class='fl'>50</span>
+<span class='va'>k_in_pop</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/Log.html'>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 class='fu'><a href='https://rdrr.io/r/base/Random.html'>set.seed</a></span><span class='op'>(</span><span class='fl'>1234</span><span class='op'>)</span>
+<span class='va'>k_in</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/Lognormal.html'>rlnorm</a></span><span class='op'>(</span><span class='fl'>5</span>, <span class='fu'><a href='https://rdrr.io/r/base/Log.html'>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 class='va'>SFO</span> <span class='op'>&lt;-</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 class='va'>pred_sfo</span> <span class='op'>&lt;-</span> <span class='kw'>function</span><span class='op'>(</span><span class='va'>k</span><span class='op'>)</span> <span class='op'>{</span>
+ <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span><span class='op'>(</span><span class='va'>SFO</span>,
+ <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent <span class='op'>=</span> <span class='va'>k</span><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>,
+ <span class='va'>sampling_times</span><span class='op'>)</span>
+<span class='op'>}</span>
+
+<span class='va'>ds_sfo_mean</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>k_in</span>, <span class='va'>pred_sfo</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_sfo_mean</span><span class='op'>)</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>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 class='fu'><a href='https://rdrr.io/r/base/Random.html'>set.seed</a></span><span class='op'>(</span><span class='fl'>12345</span><span class='op'>)</span>
+<span class='va'>ds_sfo_syn</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>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 class='fu'><a href='add_err.html'>add_err</a></span><span class='op'>(</span><span class='va'>ds</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'>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>,
+ 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 class='op'>}</span><span class='op'>)</span>
+
+<span class='co'># Evaluate using mmkin and nlme</span>
+<span class='kw'><a href='https://rdrr.io/r/base/library.html'>library</a></span><span class='op'>(</span><span class='va'><a href='https://svn.r-project.org/R-packages/trunk/nlme/'>nlme</a></span><span class='op'>)</span>
+<span class='va'>f_mmkin</span> <span class='op'>&lt;-</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>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Optimisation did not converge:</span>
+#&gt; <span class='warning'>iteration limit reached without convergence (10)</span></div><div class='input'><span class='va'>f_nlme</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f_mmkin</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Iteration 4, LME step: nlminb() did not converge (code = 1). PORT message: false convergence (8)</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/summary.html'>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>
+</div><div class='output co'>#&gt; nlme version used for fitting: 3.1.151
+#&gt; mkin version used for pre-fitting: 1.0.0
+#&gt; R version used for fitting: 4.0.3
+#&gt; Date of fit: Wed Feb 3 17:32:05 2021
+#&gt; Date of summary: Wed Feb 3 17:32:05 2021
+#&gt;
+#&gt; Equations:
+#&gt; d_parent/dt = - k_parent * parent
+#&gt;
+#&gt; Data:
+#&gt; 90 observations of 1 variable(s) grouped in 5 datasets
+#&gt;
+#&gt; Model predictions using solution type analytical
+#&gt;
+#&gt; Fitted in 0.526 s using 4 iterations
+#&gt;
+#&gt; Variance model: Two-component variance function
+#&gt;
+#&gt; Mean of starting values for individual parameters:
+#&gt; parent_0 log_k_parent
+#&gt; 101.569 -4.454
+#&gt;
+#&gt; Fixed degradation parameter values:
+#&gt; None
+#&gt;
+#&gt; Results:
+#&gt;
+#&gt; AIC BIC logLik
+#&gt; 584.5 599.5 -286.2
+#&gt;
+#&gt; Optimised, transformed parameters with symmetric confidence intervals:
+#&gt; lower est. upper
+#&gt; parent_0 99.371 101.592 103.814
+#&gt; log_k_parent -4.973 -4.449 -3.926
+#&gt;
+#&gt; Correlation:
+#&gt; prnt_0
+#&gt; log_k_parent 0.051
+#&gt;
+#&gt; Random effects:
+#&gt; Formula: list(parent_0 ~ 1, log_k_parent ~ 1)
+#&gt; Level: ds
+#&gt; Structure: Diagonal
+#&gt; parent_0 log_k_parent Residual
+#&gt; StdDev: 6.91e-05 0.5863 1
+#&gt;
+#&gt; Variance function:
+#&gt; Structure: Constant plus proportion of variance covariate
+#&gt; Formula: ~fitted(.)
+#&gt; Parameter estimates:
+#&gt; const prop
+#&gt; 0.0001206605 0.0789967776
+#&gt;
+#&gt; Backtransformed parameters with asymmetric confidence intervals:
+#&gt; lower est. upper
+#&gt; parent_0 99.370883 101.59243 103.81398
+#&gt; k_parent 0.006923 0.01168 0.01972
+#&gt;
+#&gt; Estimated disappearance times:
+#&gt; DT50 DT90
+#&gt; parent 59.32 197.1
+#&gt;
+#&gt; Data:
+#&gt; ds name time observed predicted residual std standardized
+#&gt; ds 1 parent 0 104.1 101.592 2.50757 8.0255 0.312451
+#&gt; ds 1 parent 0 105.0 101.592 3.40757 8.0255 0.424594
+#&gt; ds 1 parent 1 98.5 100.796 -2.29571 7.9625 -0.288314
+#&gt; ds 1 parent 1 96.1 100.796 -4.69571 7.9625 -0.589725
+#&gt; ds 1 parent 3 101.9 99.221 2.67904 7.8381 0.341796
+#&gt; ds 1 parent 3 85.2 99.221 -14.02096 7.8381 -1.788813
+#&gt; ds 1 parent 7 99.1 96.145 2.95512 7.5951 0.389081
+#&gt; ds 1 parent 7 93.0 96.145 -3.14488 7.5951 -0.414065
+#&gt; ds 1 parent 14 88.1 90.989 -2.88944 7.1879 -0.401988
+#&gt; ds 1 parent 14 84.1 90.989 -6.88944 7.1879 -0.958480
+#&gt; ds 1 parent 28 80.2 81.493 -1.29305 6.4377 -0.200857
+#&gt; ds 1 parent 28 91.3 81.493 9.80695 6.4377 1.523365
+#&gt; ds 1 parent 60 65.1 63.344 1.75642 5.0039 0.351008
+#&gt; ds 1 parent 60 65.8 63.344 2.45642 5.0039 0.490898
+#&gt; ds 1 parent 90 47.8 50.018 -2.21764 3.9512 -0.561253
+#&gt; ds 1 parent 90 53.5 50.018 3.48236 3.9512 0.881335
+#&gt; ds 1 parent 120 37.6 39.495 -1.89515 3.1200 -0.607423
+#&gt; ds 1 parent 120 39.3 39.495 -0.19515 3.1200 -0.062549
+#&gt; ds 2 parent 0 107.9 101.592 6.30757 8.0255 0.785944
+#&gt; ds 2 parent 0 102.1 101.592 0.50757 8.0255 0.063245
+#&gt; ds 2 parent 1 103.8 100.058 3.74159 7.9043 0.473362
+#&gt; ds 2 parent 1 108.6 100.058 8.54159 7.9043 1.080627
+#&gt; ds 2 parent 3 91.0 97.060 -6.05952 7.6674 -0.790297
+#&gt; ds 2 parent 3 84.9 97.060 -12.15952 7.6674 -1.585874
+#&gt; ds 2 parent 7 79.3 91.329 -12.02867 7.2147 -1.667252
+#&gt; ds 2 parent 7 100.9 91.329 9.57133 7.2147 1.326648
+#&gt; ds 2 parent 14 77.3 82.102 -4.80185 6.4858 -0.740366
+#&gt; ds 2 parent 14 83.5 82.102 1.39815 6.4858 0.215571
+#&gt; ds 2 parent 28 66.8 66.351 0.44945 5.2415 0.085748
+#&gt; ds 2 parent 28 63.3 66.351 -3.05055 5.2415 -0.582002
+#&gt; ds 2 parent 60 40.8 40.775 0.02474 3.2211 0.007679
+#&gt; ds 2 parent 60 44.8 40.775 4.02474 3.2211 1.249486
+#&gt; ds 2 parent 90 27.8 25.832 1.96762 2.0407 0.964198
+#&gt; ds 2 parent 90 27.0 25.832 1.16762 2.0407 0.572171
+#&gt; ds 2 parent 120 15.2 16.366 -1.16561 1.2928 -0.901596
+#&gt; ds 2 parent 120 15.5 16.366 -0.86561 1.2928 -0.669547
+#&gt; ds 3 parent 0 97.7 101.592 -3.89243 8.0255 -0.485009
+#&gt; ds 3 parent 0 88.2 101.592 -13.39243 8.0255 -1.668740
+#&gt; ds 3 parent 1 109.9 99.218 10.68196 7.8379 1.362859
+#&gt; ds 3 parent 1 97.8 99.218 -1.41804 7.8379 -0.180921
+#&gt; ds 3 parent 3 100.5 94.634 5.86555 7.4758 0.784603
+#&gt; ds 3 parent 3 77.4 94.634 -17.23445 7.4758 -2.305360
+#&gt; ds 3 parent 7 78.3 86.093 -7.79273 6.8010 -1.145813
+#&gt; ds 3 parent 7 90.3 86.093 4.20727 6.8010 0.618621
+#&gt; ds 3 parent 14 76.0 72.958 3.04222 5.7634 0.527849
+#&gt; ds 3 parent 14 79.1 72.958 6.14222 5.7634 1.065723
+#&gt; ds 3 parent 28 46.0 52.394 -6.39404 4.1390 -1.544842
+#&gt; ds 3 parent 28 53.4 52.394 1.00596 4.1390 0.243046
+#&gt; ds 3 parent 60 25.1 24.582 0.51786 1.9419 0.266676
+#&gt; ds 3 parent 60 21.4 24.582 -3.18214 1.9419 -1.638665
+#&gt; ds 3 parent 90 11.0 12.092 -1.09202 0.9552 -1.143200
+#&gt; ds 3 parent 90 14.2 12.092 2.10798 0.9552 2.206777
+#&gt; ds 3 parent 120 5.8 5.948 -0.14810 0.4699 -0.315178
+#&gt; ds 3 parent 120 6.1 5.948 0.15190 0.4699 0.323282
+#&gt; ds 4 parent 0 95.3 101.592 -6.29243 8.0255 -0.784057
+#&gt; ds 4 parent 0 102.0 101.592 0.40757 8.0255 0.050785
+#&gt; ds 4 parent 1 104.4 101.125 3.27549 7.9885 0.410025
+#&gt; ds 4 parent 1 105.4 101.125 4.27549 7.9885 0.535205
+#&gt; ds 4 parent 3 113.7 100.195 13.50487 7.9151 1.706218
+#&gt; ds 4 parent 3 82.3 100.195 -17.89513 7.9151 -2.260887
+#&gt; ds 4 parent 7 98.1 98.362 -0.26190 7.7703 -0.033706
+#&gt; ds 4 parent 7 87.8 98.362 -10.56190 7.7703 -1.359270
+#&gt; ds 4 parent 14 97.9 95.234 2.66590 7.5232 0.354357
+#&gt; ds 4 parent 14 104.8 95.234 9.56590 7.5232 1.271522
+#&gt; ds 4 parent 28 85.0 89.274 -4.27372 7.0523 -0.606001
+#&gt; ds 4 parent 28 77.2 89.274 -12.07372 7.0523 -1.712017
+#&gt; ds 4 parent 60 82.2 77.013 5.18661 6.0838 0.852526
+#&gt; ds 4 parent 60 86.1 77.013 9.08661 6.0838 1.493571
+#&gt; ds 4 parent 90 70.5 67.053 3.44692 5.2970 0.650733
+#&gt; ds 4 parent 90 61.7 67.053 -5.35308 5.2970 -1.010591
+#&gt; ds 4 parent 120 60.0 58.381 1.61905 4.6119 0.351058
+#&gt; ds 4 parent 120 56.4 58.381 -1.98095 4.6119 -0.429530
+#&gt; ds 5 parent 0 92.6 101.592 -8.99243 8.0255 -1.120486
+#&gt; ds 5 parent 0 116.5 101.592 14.90757 8.0255 1.857531
+#&gt; ds 5 parent 1 108.0 99.914 8.08560 7.8929 1.024413
+#&gt; ds 5 parent 1 104.9 99.914 4.98560 7.8929 0.631656
+#&gt; ds 5 parent 3 100.5 96.641 3.85898 7.6343 0.505477
+#&gt; ds 5 parent 3 89.5 96.641 -7.14102 7.6343 -0.935383
+#&gt; ds 5 parent 7 91.7 90.412 1.28752 7.1423 0.180267
+#&gt; ds 5 parent 7 95.1 90.412 4.68752 7.1423 0.656305
+#&gt; ds 5 parent 14 82.2 80.463 1.73715 6.3563 0.273296
+#&gt; ds 5 parent 14 84.5 80.463 4.03715 6.3563 0.635141
+#&gt; ds 5 parent 28 60.5 63.728 -3.22788 5.0343 -0.641178
+#&gt; ds 5 parent 28 72.8 63.728 9.07212 5.0343 1.802063
+#&gt; ds 5 parent 60 38.3 37.399 0.90061 2.9544 0.304835
+#&gt; ds 5 parent 60 40.7 37.399 3.30061 2.9544 1.117174
+#&gt; ds 5 parent 90 22.5 22.692 -0.19165 1.7926 -0.106913
+#&gt; ds 5 parent 90 20.8 22.692 -1.89165 1.7926 -1.055273
+#&gt; ds 5 parent 120 13.4 13.768 -0.36790 1.0876 -0.338259
+#&gt; ds 5 parent 120 13.8 13.768 0.03210 1.0876 0.029517</div><div class='input'>
+</div></pre>
+ </div>
+ <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+ <nav id="toc" data-toggle="toc" class="sticky-top">
+ <h2 data-toc-skip>Contents</h2>
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+
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+ <div class="copyright">
+ <p>Developed by Johannes Ranke.</p>
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+<div class="pkgdown">
+ <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
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