<!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>Function reference • 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" 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role="navigation"> <div class="container"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">mkin</a> <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.1.2</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"><li> <a href="../reference/index.html">Functions and data</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> Articles <span class="caret"></span> </a> <ul class="dropdown-menu" role="menu"><li> <a href="../articles/mkin.html">Introduction to mkin</a> </li> <li> <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> <li> <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> <a href="../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> </li> <li> <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> </li> <li> <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> </li> <li> <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> </li> <li> <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a> </li> </ul></li> <li> <a href="../news/index.html">News</a> </li> </ul><ul class="nav navbar-nav navbar-right"><li> <a href="https://github.com/jranke/mkin/" class="external-link"> <span class="fab fa-github fa-lg"></span> </a> </li> </ul></div><!--/.nav-collapse --> </div><!--/.container --> </div><!--/.navbar --> </header><div class="row"> <div class="contents col-md-9"> <div class="page-header"> <h1>Reference</h1> </div> <table class="ref-index"><colgroup><col class="alias"><col class="title"></colgroup><tbody><tr><th colspan="2"> <h2 id="main-functions">Main functions <a href="#main-functions" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p><p>Essential functionality</p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="mkinmod.html">mkinmod()</a></code> <code><a href="mkinmod.html">print(<i><mkinmod></i>)</a></code> <code><a href="mkinmod.html">mkinsub()</a></code> </p> </td> <td><p>Function to set up a kinetic model with one or more state variables</p></td> </tr><tr><td> <p><code><a href="mkinfit.html">mkinfit()</a></code> </p> </td> <td><p>Fit a kinetic model to data with one or more state variables</p></td> </tr><tr><td> <p><code><a href="mmkin.html">mmkin()</a></code> <code><a href="mmkin.html">print(<i><mmkin></i>)</a></code> </p> </td> <td><p>Fit one or more kinetic models with one or more state variables to one or more datasets</p></td> </tr><tr><td> <p><code><a href="mhmkin.html">mhmkin()</a></code> <code><a href="mhmkin.html">`[`(<i><mhmkin></i>)</a></code> <code><a href="mhmkin.html">print(<i><mhmkin></i>)</a></code> </p> </td> <td><p>Fit nonlinear mixed-effects models built from one or more kinetic degradation models and one or more error models</p></td> </tr></tbody><tbody><tr><th colspan="2"> <h2 id="generics">Generics <a href="#generics" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p><p>Generic functions introduced by the package</p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="convergence.html">convergence()</a></code> <code><a href="convergence.html">print(<i><convergence.mmkin></i>)</a></code> </p> </td> <td><p>Method to get convergence information</p></td> </tr><tr><td> <p><code><a href="illparms.html">illparms()</a></code> <code><a href="illparms.html">print(<i><illparms.mmkin></i>)</a></code> <code><a href="illparms.html">print(<i><illparms.mhmkin></i>)</a></code> </p> </td> <td><p>Method to get the names of ill-defined parameters</p></td> </tr><tr><td> <p><code><a href="endpoints.html">endpoints()</a></code> </p> </td> <td><p>Function to calculate endpoints for further use from kinetic models fitted with mkinfit</p></td> </tr></tbody><tbody><tr><th colspan="2"> <h2 id="show-results">Show results <a href="#show-results" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p><p>Functions working with mkinfit objects</p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="plot.mkinfit.html">plot(<i><mkinfit></i>)</a></code> <code><a href="plot.mkinfit.html">plot_sep()</a></code> <code><a href="plot.mkinfit.html">plot_res()</a></code> <code><a href="plot.mkinfit.html">plot_err()</a></code> </p> </td> <td><p>Plot the observed data and the fitted model of an mkinfit object</p></td> </tr><tr><td> <p><code><a href="summary.mkinfit.html">summary(<i><mkinfit></i>)</a></code> <code><a href="summary.mkinfit.html">print(<i><summary.mkinfit></i>)</a></code> </p> </td> <td><p>Summary method for class "mkinfit"</p></td> </tr><tr><td> <p><code><a href="parms.html">parms()</a></code> </p> </td> <td><p>Extract model parameters from mkinfit models</p></td> </tr><tr><td> <p><code><a href="confint.mkinfit.html">confint(<i><mkinfit></i>)</a></code> </p> </td> <td><p>Confidence intervals for parameters of mkinfit objects</p></td> </tr><tr><td> <p><code><a href="update.mkinfit.html">update(<i><mkinfit></i>)</a></code> </p> </td> <td><p>Update an mkinfit model with different arguments</p></td> </tr><tr><td> <p><code><a href="lrtest.mkinfit.html">lrtest(<i><mkinfit></i>)</a></code> <code><a href="lrtest.mkinfit.html">lrtest(<i><mmkin></i>)</a></code> </p> </td> <td><p>Likelihood ratio test for mkinfit models</p></td> </tr><tr><td> <p><code><a href="loftest.html">loftest()</a></code> </p> </td> <td><p>Lack-of-fit test for models fitted to data with replicates</p></td> </tr><tr><td> <p><code><a href="mkinerrmin.html">mkinerrmin()</a></code> </p> </td> <td><p>Calculate the minimum error to assume in order to pass the variance test</p></td> </tr><tr><td> <p><code><a href="aw.html">aw()</a></code> </p> </td> <td><p>Calculate Akaike weights for model averaging</p></td> </tr><tr><td> <p><code><a href="CAKE_export.html">CAKE_export()</a></code> </p> </td> <td><p>Export a list of datasets format to a CAKE study file</p></td> </tr></tbody><tbody><tr><th colspan="2"> <h2 id="work-with-mmkin-objects">Work with mmkin objects <a href="#work-with-mmkin-objects" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p><p>Functions working with aggregated results</p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="Extract.mmkin.html">`[`(<i><mmkin></i>)</a></code> </p> </td> <td><p>Subsetting method for mmkin objects</p></td> </tr><tr><td> <p><code><a href="plot.mmkin.html">plot(<i><mmkin></i>)</a></code> </p> </td> <td><p>Plot model fits (observed and fitted) and the residuals for a row or column of an mmkin object</p></td> </tr><tr><td> <p><code><a href="AIC.mmkin.html">AIC(<i><mmkin></i>)</a></code> <code><a href="AIC.mmkin.html">BIC(<i><mmkin></i>)</a></code> </p> </td> <td><p>Calculate the AIC for a column of an mmkin object</p></td> </tr><tr><td> <p><code><a href="summary.mmkin.html">summary(<i><mmkin></i>)</a></code> <code><a href="summary.mmkin.html">print(<i><summary.mmkin></i>)</a></code> </p> </td> <td><p>Summary method for class "mmkin"</p></td> </tr></tbody><tbody><tr><th colspan="2"> <h2 id="mixed-models">Mixed models <a href="#mixed-models" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p><p>Create and work with nonlinear hierarchical models</p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="nlme.mmkin.html">nlme(<i><mmkin></i>)</a></code> <code><a href="nlme.mmkin.html">print(<i><nlme.mmkin></i>)</a></code> <code><a href="nlme.mmkin.html">update(<i><nlme.mmkin></i>)</a></code> </p> </td> <td><p>Create an nlme model for an mmkin row object</p></td> </tr><tr><td> <p><code><a href="saem.html">saem()</a></code> <code><a href="saem.html">print(<i><saem.mmkin></i>)</a></code> <code><a href="saem.html">saemix_model()</a></code> <code><a href="saem.html">saemix_data()</a></code> </p> </td> <td><p>Fit nonlinear mixed models with SAEM</p></td> </tr><tr><td> <p><code><a href="mhmkin.html">mhmkin()</a></code> <code><a href="mhmkin.html">`[`(<i><mhmkin></i>)</a></code> <code><a href="mhmkin.html">print(<i><mhmkin></i>)</a></code> </p> </td> <td><p>Fit nonlinear mixed-effects models built from one or more kinetic degradation models and one or more error models</p></td> </tr><tr><td> <p><code><a href="plot.mixed.mmkin.html">plot(<i><mixed.mmkin></i>)</a></code> </p> </td> <td><p>Plot predictions from a fitted nonlinear mixed model obtained via an mmkin row object</p></td> </tr><tr><td> <p><code><a href="summary.nlme.mmkin.html">summary(<i><nlme.mmkin></i>)</a></code> <code><a href="summary.nlme.mmkin.html">print(<i><summary.nlme.mmkin></i>)</a></code> </p> </td> <td><p>Summary method for class "nlme.mmkin"</p></td> </tr><tr><td> <p><code><a href="summary.saem.mmkin.html">summary(<i><saem.mmkin></i>)</a></code> <code><a href="summary.saem.mmkin.html">print(<i><summary.saem.mmkin></i>)</a></code> </p> </td> <td><p>Summary method for class "saem.mmkin"</p></td> </tr><tr><td> <p><code><a href="nlme.html">nlme_function()</a></code> <code><a href="nlme.html">nlme_data()</a></code> </p> </td> <td><p>Helper functions to create nlme models from mmkin row objects</p></td> </tr><tr><td> <p><code><a href="get_deg_func.html">get_deg_func()</a></code> </p> </td> <td><p>Retrieve a degradation function from the mmkin namespace</p></td> </tr><tr><td> <p><code><a href="mixed.html">mixed()</a></code> <code><a href="mixed.html">print(<i><mixed.mmkin></i>)</a></code> </p> </td> <td><p>Create a mixed effects model from an mmkin row object</p></td> </tr><tr><td> <p><code><a href="reexports.html">reexports</a></code> <code><a href="reexports.html">intervals</a></code> <code><a href="reexports.html">lrtest</a></code> <code><a href="reexports.html">nlme</a></code> </p> </td> <td><p>Objects exported from other packages</p></td> </tr><tr><td> <p><code><a href="intervals.saem.mmkin.html">intervals(<i><saem.mmkin></i>)</a></code> </p> </td> <td><p>Confidence intervals for parameters in saem.mmkin objects</p></td> </tr></tbody><tbody><tr><th colspan="2"> <h2 id="datasets-and-known-results">Datasets and known results <a href="#datasets-and-known-results" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="focus_soil_moisture.html">focus_soil_moisture</a></code> </p> </td> <td><p>FOCUS default values for soil moisture contents at field capacity, MWHC and 1/3 bar</p></td> </tr><tr><td> <p><code><a href="D24_2014.html">D24_2014</a></code> </p> </td> <td><p>Aerobic soil degradation data on 2,4-D from the EU assessment in 2014</p></td> </tr><tr><td> <p><code><a href="dimethenamid_2018.html">dimethenamid_2018</a></code> </p> </td> <td><p>Aerobic soil degradation data on dimethenamid and dimethenamid-P from the EU assessment in 2018</p></td> </tr><tr><td> <p><code><a href="FOCUS_2006_datasets.html">FOCUS_2006_A</a></code> <code><a href="FOCUS_2006_datasets.html">FOCUS_2006_B</a></code> <code><a href="FOCUS_2006_datasets.html">FOCUS_2006_C</a></code> <code><a href="FOCUS_2006_datasets.html">FOCUS_2006_D</a></code> <code><a href="FOCUS_2006_datasets.html">FOCUS_2006_E</a></code> <code><a href="FOCUS_2006_datasets.html">FOCUS_2006_F</a></code> </p> </td> <td><p>Datasets A to F from the FOCUS Kinetics report from 2006</p></td> </tr><tr><td> <p><code><a href="FOCUS_2006_SFO_ref_A_to_F.html">FOCUS_2006_SFO_ref_A_to_F</a></code> </p> </td> <td><p>Results of fitting the SFO model to Datasets A to F of FOCUS (2006)</p></td> </tr><tr><td> <p><code><a href="FOCUS_2006_FOMC_ref_A_to_F.html">FOCUS_2006_FOMC_ref_A_to_F</a></code> </p> </td> <td><p>Results of fitting the FOMC model to Datasets A to F of FOCUS (2006)</p></td> </tr><tr><td> <p><code><a href="FOCUS_2006_HS_ref_A_to_F.html">FOCUS_2006_HS_ref_A_to_F</a></code> </p> </td> <td><p>Results of fitting the HS model to Datasets A to F of FOCUS (2006)</p></td> </tr><tr><td> <p><code><a href="FOCUS_2006_DFOP_ref_A_to_B.html">FOCUS_2006_DFOP_ref_A_to_B</a></code> </p> </td> <td><p>Results of fitting the DFOP model to Datasets A to B of FOCUS (2006)</p></td> </tr><tr><td> <p><code><a href="NAFTA_SOP_2015.html">NAFTA_SOP_Appendix_B</a></code> <code><a href="NAFTA_SOP_2015.html">NAFTA_SOP_Appendix_D</a></code> </p> </td> <td><p>Example datasets from the NAFTA SOP published 2015</p></td> </tr><tr><td> <p><code><a href="NAFTA_SOP_Attachment.html">NAFTA_SOP_Attachment</a></code> </p> </td> <td><p>Example datasets from Attachment 1 to the NAFTA SOP published 2015</p></td> </tr><tr><td> <p><code><a href="mccall81_245T.html">mccall81_245T</a></code> </p> </td> <td><p>Datasets on aerobic soil metabolism of 2,4,5-T in six soils</p></td> </tr><tr><td> <p><code><a href="schaefer07_complex_case.html">schaefer07_complex_case</a></code> </p> </td> <td><p>Metabolism data set used for checking the software quality of KinGUI</p></td> </tr><tr><td> <p><code><a href="synthetic_data_for_UBA_2014.html">synthetic_data_for_UBA_2014</a></code> </p> </td> <td><p>Synthetic datasets for one parent compound with two metabolites</p></td> </tr><tr><td> <p><code><a href="experimental_data_for_UBA.html">experimental_data_for_UBA_2019</a></code> </p> </td> <td><p>Experimental datasets used for development and testing of error models</p></td> </tr><tr><td> <p><code><a href="test_data_from_UBA_2014.html">test_data_from_UBA_2014</a></code> </p> </td> <td><p>Three experimental datasets from two water sediment systems and one soil</p></td> </tr><tr><td> <p><code><a href="mkinds.html">print(<i><mkinds></i>)</a></code> </p> </td> <td><p>A dataset class for mkin</p></td> </tr><tr><td> <p><code><a href="mkindsg.html">print(<i><mkindsg></i>)</a></code> </p> </td> <td><p>A class for dataset groups for mkin</p></td> </tr></tbody><tbody><tr><th colspan="2"> <h2 id="nafta-guidance">NAFTA guidance <a href="#nafta-guidance" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="nafta.html">nafta()</a></code> <code><a href="nafta.html">print(<i><nafta></i>)</a></code> </p> </td> <td><p>Evaluate parent kinetics using the NAFTA guidance</p></td> </tr><tr><td> <p><code><a href="plot.nafta.html">plot(<i><nafta></i>)</a></code> </p> </td> <td><p>Plot the results of the three models used in the NAFTA scheme.</p></td> </tr></tbody><tbody><tr><th colspan="2"> <h2 id="utility-functions">Utility functions <a href="#utility-functions" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="f_time_norm_focus.html">f_time_norm_focus()</a></code> </p> </td> <td><p>Normalisation factors for aerobic soil degradation according to FOCUS guidance</p></td> </tr><tr><td> <p><code><a href="max_twa_parent.html">max_twa_parent()</a></code> <code><a href="max_twa_parent.html">max_twa_sfo()</a></code> <code><a href="max_twa_parent.html">max_twa_fomc()</a></code> <code><a href="max_twa_parent.html">max_twa_dfop()</a></code> <code><a href="max_twa_parent.html">max_twa_hs()</a></code> </p> </td> <td><p>Function to calculate maximum time weighted average concentrations from kinetic models fitted with mkinfit</p></td> </tr><tr><td> <p><code><a href="mkin_wide_to_long.html">mkin_wide_to_long()</a></code> </p> </td> <td><p>Convert a dataframe with observations over time into long format</p></td> </tr><tr><td> <p><code><a href="mkin_long_to_wide.html">mkin_long_to_wide()</a></code> </p> </td> <td><p>Convert a dataframe from long to wide format</p></td> </tr></tbody><tbody><tr><th colspan="2"> <h2 id="helper-functions-mainly-used-internally">Helper functions mainly used internally <a href="#helper-functions-mainly-used-internally" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="mkinpredict.html">mkinpredict()</a></code> </p> </td> <td><p>Produce predictions from a kinetic model using specific parameters</p></td> </tr><tr><td> <p><code><a href="transform_odeparms.html">transform_odeparms()</a></code> <code><a href="transform_odeparms.html">backtransform_odeparms()</a></code> </p> </td> <td><p>Functions to transform and backtransform kinetic parameters for fitting</p></td> </tr><tr><td> <p><code><a href="ilr.html">ilr()</a></code> <code><a href="ilr.html">invilr()</a></code> </p> </td> <td><p>Function to perform isometric log-ratio transformation</p></td> </tr><tr><td> <p><code><a href="logLik.mkinfit.html">logLik(<i><mkinfit></i>)</a></code> </p> </td> <td><p>Calculated the log-likelihood of a fitted mkinfit object</p></td> </tr><tr><td> <p><code><a href="residuals.mkinfit.html">residuals(<i><mkinfit></i>)</a></code> </p> </td> <td><p>Extract residuals from an mkinfit model</p></td> </tr><tr><td> <p><code><a href="nobs.mkinfit.html">nobs(<i><mkinfit></i>)</a></code> </p> </td> <td><p>Number of observations on which an mkinfit object was fitted</p></td> </tr><tr><td> <p><code><a href="mkinresplot.html">mkinresplot()</a></code> </p> </td> <td><p>Function to plot residuals stored in an mkin object</p></td> </tr><tr><td> <p><code><a href="mkinparplot.html">mkinparplot()</a></code> </p> </td> <td><p>Function to plot the confidence intervals obtained using mkinfit</p></td> </tr><tr><td> <p><code><a href="mkinerrplot.html">mkinerrplot()</a></code> </p> </td> <td><p>Function to plot squared residuals and the error model for an mkin object</p></td> </tr><tr><td> <p><code><a href="mean_degparms.html">mean_degparms()</a></code> </p> </td> <td><p>Calculate mean degradation parameters for an mmkin row object</p></td> </tr><tr><td> <p><code><a href="create_deg_func.html">create_deg_func()</a></code> </p> </td> <td><p>Create degradation functions for known analytical solutions</p></td> </tr></tbody><tbody><tr><th colspan="2"> <h2 id="analytical-solutions">Analytical solutions <a href="#analytical-solutions" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p><p>Parent only model solutions</p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="SFO.solution.html">SFO.solution()</a></code> </p> </td> <td><p>Single First-Order kinetics</p></td> </tr><tr><td> <p><code><a href="FOMC.solution.html">FOMC.solution()</a></code> </p> </td> <td><p>First-Order Multi-Compartment kinetics</p></td> </tr><tr><td> <p><code><a href="DFOP.solution.html">DFOP.solution()</a></code> </p> </td> <td><p>Double First-Order in Parallel kinetics</p></td> </tr><tr><td> <p><code><a href="SFORB.solution.html">SFORB.solution()</a></code> </p> </td> <td><p>Single First-Order Reversible Binding kinetics</p></td> </tr><tr><td> <p><code><a href="HS.solution.html">HS.solution()</a></code> </p> </td> <td><p>Hockey-Stick kinetics</p></td> </tr><tr><td> <p><code><a href="IORE.solution.html">IORE.solution()</a></code> </p> </td> <td><p>Indeterminate order rate equation kinetics</p></td> </tr><tr><td> <p><code><a href="logistic.solution.html">logistic.solution()</a></code> </p> </td> <td><p>Logistic kinetics</p></td> </tr></tbody><tbody><tr><th colspan="2"> <h2 id="generate-synthetic-datasets">Generate synthetic datasets <a href="#generate-synthetic-datasets" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="add_err.html">add_err()</a></code> </p> </td> <td><p>Add normally distributed errors to simulated kinetic degradation data</p></td> </tr><tr><td> <p><code><a href="sigma_twocomp.html">sigma_twocomp()</a></code> </p> </td> <td><p>Two-component error model</p></td> </tr></tbody><tbody><tr><th colspan="2"> <h2 id="deprecated-functions">Deprecated functions <a href="#deprecated-functions" class="anchor" aria-hidden="true"></a></h2> <p class="section-desc"></p><p>Functions that have been superseded</p> </th> </tr></tbody><tbody><tr><td> <p><code><a href="mkinplot.html">mkinplot()</a></code> </p> </td> <td><p>Plot the observed data and the fitted model of an mkinfit object</p></td> </tr></tbody></table></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> </nav></div> </div> 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