diff options
Diffstat (limited to 'docs/articles/web_only/dimethenamid_2018.html')
| -rw-r--r-- | docs/articles/web_only/dimethenamid_2018.html | 93 |
1 files changed, 52 insertions, 41 deletions
diff --git a/docs/articles/web_only/dimethenamid_2018.html b/docs/articles/web_only/dimethenamid_2018.html index 09aa5150..7650f06f 100644 --- a/docs/articles/web_only/dimethenamid_2018.html +++ b/docs/articles/web_only/dimethenamid_2018.html @@ -105,7 +105,7 @@ <h1 data-toc-skip>Example evaluations of the dimethenamid data from 2018</h1> <h4 data-toc-skip class="author">Johannes Ranke</h4> - <h4 data-toc-skip class="date">Last change 7 March 2022, built on 16 Mar 2022</h4> + <h4 data-toc-skip class="date">Last change 7 March 2022, built on 18 May 2022</h4> <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/dimethenamid_2018.rmd" class="external-link"><code>vignettes/web_only/dimethenamid_2018.rmd</code></a></small> <div class="hidden name"><code>dimethenamid_2018.rmd</code></div> @@ -178,7 +178,7 @@ Status of individual fits: dataset model Calke Borstel Flaach BBA 2.2 BBA 2.3 Elliot - DFOP OK OK C OK C OK + DFOP OK OK OK OK C OK OK: No warnings C: Optimisation did not converge: @@ -231,32 +231,41 @@ f_parent_nlme_dfop_tc 3 10 671.91 702.34 -325.96 2 vs 3 134.69 <.0001 <p>The saemix package provided the first Open Source implementation of the Stochastic Approximation to the Expectation Maximisation (SAEM) algorithm. SAEM fits of degradation models can be conveniently performed using an interface to the saemix package available in current development versions of the mkin package.</p> <p>The corresponding SAEM fits of the four combinations of degradation and error models are fitted below. As there is no convergence criterion implemented in the saemix package, the convergence plots need to be manually checked for every fit. We define control settings that work well for all the parent data fits shown in this vignette.</p> <div class="sourceCode" id="cb14"><pre class="downlit sourceCode r"> -<code class="sourceCode R"><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">saemix</span><span class="op">)</span> -<span class="va">saemix_control</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <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">800</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>, +<code class="sourceCode R"><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">saemix</span><span class="op">)</span></code></pre></div> +<pre><code>Loading required package: npde</code></pre> +<pre><code>Package saemix, version 3.0 + please direct bugs, questions and feedback to emmanuelle.comets@inserm.fr</code></pre> +<pre><code> +Attaching package: 'saemix'</code></pre> +<pre><code>The following objects are masked from 'package:npde': + + kurtosis, skewness</code></pre> +<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span class="va">saemix_control</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <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">800</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>, print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="va">saemix_control_moreiter</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <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">1600</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>, print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="va">saemix_control_10k</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/saemixControl.html" class="external-link">saemixControl</a></span><span class="op">(</span>nbiter.saemix <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">10000</span>, <span class="fl">300</span><span class="op">)</span>, nb.chains <span class="op">=</span> <span class="fl">15</span>, print <span class="op">=</span> <span class="cn">FALSE</span>, save <span class="op">=</span> <span class="cn">FALSE</span>, save.graphs <span class="op">=</span> <span class="cn">FALSE</span>, displayProgress <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></code></pre></div> <p>The convergence plot for the SFO model using constant variance is shown below.</p> -<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span class="va">f_parent_saemix_sfo_const</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div> <p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_const-1.png" width="700"></p> <p>Obviously the selected number of iterations is sufficient to reach convergence. This can also be said for the SFO fit using the two-component error model.</p> -<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span class="va">f_parent_saemix_sfo_tc</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div> <p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_sfo_tc-1.png" width="700"></p> <p>When fitting the DFOP model with constant variance (see below), parameter convergence is not as unambiguous.</p> -<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span class="va">f_parent_saemix_dfop_const</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_const</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div> <p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_const-1.png" width="700"></p> -<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> <code class="sourceCode R"><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_parent_saemix_dfop_const</span><span class="op">)</span></code></pre></div> <pre><code>Kinetic nonlinear mixed-effects model fit by SAEM Structural model: @@ -277,21 +286,23 @@ DMTA_0 97.99583 96.50079 99.4909 k1 0.06377 0.03432 0.0932 k2 0.00848 0.00444 0.0125 g 0.95701 0.91313 1.0009 -a.1 1.82141 1.65974 1.9831 -SD.DMTA_0 1.64787 0.45779 2.8379 +a.1 1.82141 1.60516 2.0377 +SD.DMTA_0 1.64787 0.45729 2.8384 SD.k1 0.57439 0.24731 0.9015 -SD.k2 0.03296 -2.50143 2.5673 -SD.g 1.10266 0.32371 1.8816</code></pre> +SD.k2 0.03296 -2.50524 2.5712 +SD.g 1.10266 0.32354 1.8818</code></pre> <p>While the other parameters converge to credible values, the variance of k2 (<code>omega2.k2</code>) converges to a very small value. The printout of the <code>saem.mmkin</code> model shows that the estimated standard deviation of k2 across the population of soils (<code>SD.k2</code>) is ill-defined, indicating overparameterisation of this model.</p> <p>When the DFOP model is fitted with the two-component error model, we also observe that the estimated variance of k2 becomes very small, while being ill-defined, as illustrated by the excessive confidence interval of <code>SD.k2</code>.</p> -<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span class="va">f_parent_saemix_dfop_tc</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, control <span class="op">=</span> <span class="va">saemix_control</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span> <span class="va">f_parent_saemix_dfop_tc_moreiter</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, - control <span class="op">=</span> <span class="va">saemix_control_moreiter</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span> -<span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div> + control <span class="op">=</span> <span class="va">saemix_control_moreiter</span>, transformations <span class="op">=</span> <span class="st">"saemix"</span><span class="op">)</span></code></pre></div> +<pre><code>Likelihood cannot be computed by Importance Sampling.</code></pre> +<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/plot-SaemixObject-ANY-method.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></code></pre></div> <p><img src="dimethenamid_2018_files/figure-html/f_parent_saemix_dfop_tc-1.png" width="700"></p> -<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r"> <code class="sourceCode R"><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_parent_saemix_dfop_tc</span><span class="op">)</span></code></pre></div> <pre><code>Kinetic nonlinear mixed-effects model fit by SAEM Structural model: @@ -307,21 +318,21 @@ Likelihood computed by importance sampling 666 664 -323 Fitted parameters: - estimate lower upper -DMTA_0 98.27617 96.3088 100.2436 -k1 0.06437 0.0337 0.0950 -k2 0.00880 0.0063 0.0113 -g 0.95249 0.9100 0.9949 -a.1 1.06161 0.8625 1.2607 -b.1 0.02967 0.0226 0.0367 -SD.DMTA_0 2.06075 0.4187 3.7028 -SD.k1 0.59357 0.2561 0.9310 -SD.k2 0.00292 -10.2960 10.3019 -SD.g 1.05725 0.3808 1.7337</code></pre> + estimate lower upper +DMTA_0 9.82e+01 96.27937 100.1783 +k1 6.41e-02 0.03333 0.0948 +k2 8.56e-03 0.00608 0.0110 +g 9.55e-01 0.91440 0.9947 +a.1 1.07e+00 0.86542 1.2647 +b.1 2.96e-02 0.02258 0.0367 +SD.DMTA_0 2.04e+00 0.40629 3.6678 +SD.k1 5.98e-01 0.25796 0.9373 +SD.k2 5.28e-04 -58.93251 58.9336 +SD.g 1.04e+00 0.36509 1.7083</code></pre> <p>Doubling the number of iterations in the first phase of the algorithm leads to a slightly lower likelihood, and therefore to slightly higher AIC and BIC values. With even more iterations, the algorithm stops with an error message. This is related to the variance of k2 approximating zero and has been submitted as a <a href="https://github.com/saemixdevelopment/saemixextension/issues/29" class="external-link">bug to the saemix package</a>, as the algorithm does not converge in this case.</p> <p>An alternative way to fit DFOP in combination with the two-component error model is to use the model formulation with transformed parameters as used per default in mkin. When using this option, convergence is slower, but eventually the algorithm stops as well with the same error message.</p> <p>The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and the version with increased iterations can be compared using the model comparison function of the saemix package:</p> -<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span class="va">AIC_parent_saemix</span> <span class="op"><-</span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/compare.saemix.html" class="external-link">compare.saemix</a></span><span class="op">(</span> <span class="va">f_parent_saemix_sfo_const</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_sfo_tc</span><span class="op">$</span><span class="va">so</span>, @@ -329,7 +340,7 @@ SD.g 1.05725 0.3808 1.7337</code></pre> <span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span>, <span class="va">f_parent_saemix_dfop_tc_moreiter</span><span class="op">$</span><span class="va">so</span><span class="op">)</span></code></pre></div> <pre><code>Likelihoods calculated by importance sampling</code></pre> -<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">AIC_parent_saemix</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span> <span class="st">"SFO const"</span>, <span class="st">"SFO tc"</span>, <span class="st">"DFOP const"</span>, <span class="st">"DFOP tc"</span>, <span class="st">"DFOP tc more iterations"</span><span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix</span><span class="op">)</span></code></pre></div> @@ -337,10 +348,10 @@ SD.g 1.05725 0.3808 1.7337</code></pre> SFO const 796.38 795.34 SFO tc 798.38 797.13 DFOP const 705.75 703.88 -DFOP tc 665.65 663.57 -DFOP tc more iterations 665.88 663.80</code></pre> +DFOP tc 665.72 663.63 +DFOP tc more iterations NaN NaN</code></pre> <p>In order to check the influence of the likelihood calculation algorithms implemented in saemix, the likelihood from Gaussian quadrature is added to the best fit, and the AIC values obtained from the three methods are compared.</p> -<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span> <span class="op"><-</span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/llgq.saemix.html" class="external-link">llgq.saemix</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc</span><span class="op">$</span><span class="va">so</span><span class="op">)</span> <span class="va">AIC_parent_saemix_methods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span> @@ -350,9 +361,9 @@ DFOP tc more iterations 665.88 663.80</code></pre> <span class="op">)</span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">AIC_parent_saemix_methods</span><span class="op">)</span></code></pre></div> <pre><code> is gq lin -665.65 665.68 665.11 </code></pre> +665.72 665.88 665.15 </code></pre> <p>The AIC values based on importance sampling and Gaussian quadrature are very similar. Using linearisation is known to be less accurate, but still gives a similar value. In order to illustrate that the comparison of the three method depends on the degree of convergence obtained in the fit, the same comparison is shown below for the fit using the defaults for the number of iterations and the number of MCMC chains.</p> -<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span class="va">f_parent_saemix_dfop_tc_defaults</span> <span class="op"><-</span> <span class="fu">mkin</span><span class="fu">::</span><span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_parent_mkin_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span> <span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span> <span class="op"><-</span> <span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/saemix/man/llgq.saemix.html" class="external-link">llgq.saemix</a></span><span class="op">(</span><span class="va">f_parent_saemix_dfop_tc_defaults</span><span class="op">$</span><span class="va">so</span><span class="op">)</span> @@ -363,14 +374,14 @@ DFOP tc more iterations 665.88 663.80</code></pre> <span class="op">)</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">AIC_parent_saemix_methods_defaults</span><span class="op">)</span></code></pre></div> <pre><code> is gq lin -668.27 718.36 666.49 </code></pre> +668.91 663.61 667.40 </code></pre> </div> </div> <div class="section level3"> <h3 id="comparison">Comparison<a class="anchor" aria-label="anchor" href="#comparison"></a> </h3> <p>The following table gives the AIC values obtained with both backend packages using the same control parameters (800 iterations burn-in, 300 iterations second phase, 15 chains). Note that</p> -<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r"> +<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r"> <code class="sourceCode R"><span class="va">AIC_all</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span> check.names <span class="op">=</span> <span class="cn">FALSE</span>, <span class="st">"Degradation model"</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="st">"SFO"</span>, <span class="st">"SFO"</span>, <span class="st">"DFOP"</span>, <span class="st">"DFOP"</span><span class="op">)</span>, @@ -395,7 +406,7 @@ DFOP tc more iterations 665.88 663.80</code></pre> <td align="left">SFO</td> <td align="left">const</td> <td align="right">796.60</td> -<td align="right">796.60</td> +<td align="right">794.17</td> <td align="right">796.38</td> </tr> <tr class="even"> @@ -409,15 +420,15 @@ DFOP tc more iterations 665.88 663.80</code></pre> <td align="left">DFOP</td> <td align="left">const</td> <td align="right">NA</td> -<td align="right">671.98</td> +<td align="right">704.95</td> <td align="right">705.75</td> </tr> <tr class="even"> <td align="left">DFOP</td> <td align="left">tc</td> <td align="right">671.91</td> -<td align="right">665.11</td> -<td align="right">665.65</td> +<td align="right">665.15</td> +<td align="right">665.72</td> </tr> </tbody> </table> @@ -464,7 +475,7 @@ DFOP tc more iterations 665.88 663.80</code></pre> <div class="pkgdown"> <p></p> -<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.2.</p> +<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.3.</p> </div> </footer> |