Improve docs of multistart method

1 files changed, 22 insertions, 38 deletions

diff --git a/docs/dev/articles/web_only/multistart.html b/docs/dev/articles/web_only/multistart.html
index d3d9d76d..b5635df2 100644
--- a/docs/dev/articles/web_only/multistart.html
+++ b/docs/dev/articles/web_only/multistart.html
@@ -127,15 +127,13 @@
 
       
 
-      </header><div class="row">
+      </header><script src="multistart_files/accessible-code-block-0.0.1/empty-anchor.js"></script><div class="row">
   <div class="col-md-9 contents">
     <div class="page-header toc-ignore">
       <h1 data-toc-skip>Short demo of the multistart method</h1>
-                        <h4 data-toc-skip class="author">Johannes
-Ranke</h4>
+                        <h4 data-toc-skip class="author">Johannes Ranke</h4>
             
-            <h4 data-toc-skip class="date">Last change 26 September 2022
-(rebuilt 2023-04-16)</h4>
+            <h4 data-toc-skip class="date">Last change 17 April 2023 (rebuilt 2023-04-17)</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/multistart.rmd" class="external-link"><code>vignettes/web_only/multistart.rmd</code></a></small>
       <div class="hidden name"><code>multistart.rmd</code></div>
@@ -144,8 +142,7 @@ Ranke</h4>
 
     
     
-<p>The dimethenamid data from 2018 from seven soils is used as example
-data in this vignette.</p>
+<p>The dimethenamid data from 2018 from seven soils is used as example data in this vignette.</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><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://pkgdown.jrwb.de/mkin/">mkin</a></span><span class="op">)</span></span>
 <span><span class="va">dmta_ds</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span>
@@ -157,54 +154,41 @@ data in this vignette.</p>
 <span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span>
 <span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span>
 <span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="cn">NULL</span></span></code></pre></div>
-<p>First, we check the DFOP model with the two-component error model and
-random effects for all degradation parameters.</p>
+<p>First, we check the DFOP model with the two-component error model and random effects for all degradation parameters.</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">f_mmkin</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>, cores <span class="op">=</span> <span class="fl">7</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="va">f_saem_full</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">f_mmkin</span><span class="op">)</span></span>
 <span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_full</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] "sd(log_k2)"</span></span></code></pre>
-<p>We see that not all variability parameters are identifiable. The
-<code>illparms</code> function tells us that the confidence interval for
-the standard deviation of ‘log_k2’ includes zero. We check this
-assessment using multiple runs with different starting values.</p>
+<p>We see that not all variability parameters are identifiable. The <code>illparms</code> function tells us that the confidence interval for the standard deviation of ‘log_k2’ includes zero. We check this assessment using multiple runs with different starting values.</p>
 <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">f_saem_full_multi</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_full</span>, n <span class="op">=</span> <span class="fl">16</span>, cores <span class="op">=</span> <span class="fl">16</span><span class="op">)</span></span>
-<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_full_multi</span><span class="op">)</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">f_saem_full_multi</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_full</span>, n <span class="op">=</span> <span class="fl">16</span>, cores <span class="op">=</span> <span class="fl">8</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_full_multi</span>, lpos <span class="op">=</span> <span class="st">"topleft"</span><span class="op">)</span></span></code></pre></div>
 <p><img src="multistart_files/figure-html/unnamed-chunk-3-1.png" width="700"></p>
-<p>This confirms that the variance of k2 is the most problematic
-parameter, so we reduce the parameter distribution model by removing the
-intersoil variability for k2.</p>
+<p>This confirms that the variance of k2 is the most problematic parameter, so we reduce the parameter distribution model by removing the intersoil variability for k2.</p>
 <div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">f_saem_reduced</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_saem_full</span>, no_random_effect <span class="op">=</span> <span class="st">"log_k2"</span><span class="op">)</span></span>
 <span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_reduced</span><span class="op">)</span></span>
-<span><span class="va">f_saem_reduced_multi</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_reduced</span>, n <span class="op">=</span> <span class="fl">16</span>, cores <span class="op">=</span> <span class="fl">16</span><span class="op">)</span></span>
-<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span>, lpos <span class="op">=</span> <span class="st">"topright"</span><span class="op">)</span></span></code></pre></div>
+<span><span class="va">f_saem_reduced_multi</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../reference/multistart.html">multistart</a></span><span class="op">(</span><span class="va">f_saem_reduced</span>, n <span class="op">=</span> <span class="fl">16</span>, cores <span class="op">=</span> <span class="fl">8</span><span class="op">)</span></span>
+<span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span>, lpos <span class="op">=</span> <span class="st">"topright"</span>, ylim <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">0.5</span>, <span class="fl">2</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <p><img src="multistart_files/figure-html/unnamed-chunk-4-1.png" width="700"></p>
-<p>The results confirm that all remaining parameters can be determined
-with sufficient certainty.</p>
-<p>We can also analyse the log-likelihoods obtained in the multiple
-runs:</p>
+<p>The results confirm that all remaining parameters can be determined with sufficient certainty.</p>
+<p>We can also analyse the log-likelihoods obtained in the multiple runs:</p>
 <div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../../reference/llhist.html">llhist</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span><span class="op">)</span></span></code></pre></div>
 <p><img src="multistart_files/figure-html/unnamed-chunk-5-1.png" width="700"></p>
-<p>The parameter histograms can be further improved by excluding the
-result with the low likelihood.</p>
+<p>We can use the <code>anova</code> method to compare the models.</p>
 <div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../../reference/parplot.html">parplot</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span>, lpos <span class="op">=</span> <span class="st">"topright"</span>, llmin <span class="op">=</span> <span class="op">-</span><span class="fl">326</span>, ylim <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">0.5</span>, <span class="fl">2</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<p><img src="multistart_files/figure-html/unnamed-chunk-6-1.png" width="700"></p>
-<p>We can use the <code>anova</code> method to compare the models,
-including a likelihood ratio test if the models are nested.</p>
-<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_full</span>, <span class="fu"><a href="../../reference/multistart.html">best</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span><span class="op">)</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_full</span>, <span class="fu"><a href="../../reference/multistart.html">best</a></span><span class="op">(</span><span class="va">f_saem_full_multi</span><span class="op">)</span>,</span>
+<span>  <span class="va">f_saem_reduced</span>, <span class="fu"><a href="../../reference/multistart.html">best</a></span><span class="op">(</span><span class="va">f_saem_reduced_multi</span><span class="op">)</span>, test <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Data: 155 observations of 1 variable(s) grouped in 6 datasets</span></span>
 <span><span class="co">## </span></span>
-<span><span class="co">##                            npar    AIC    BIC     Lik Chisq Df Pr(&gt;Chisq)</span></span>
-<span><span class="co">## best(f_saem_reduced_multi)    9 663.69 661.82 -322.85                    </span></span>
-<span><span class="co">## f_saem_full                  10 669.77 667.69 -324.89     0  1          1</span></span></code></pre>
-<p>While AIC and BIC are lower for the reduced model, the likelihood
-ratio test does not indicate a significant difference between the
-fits.</p>
+<span><span class="co">##                            npar    AIC    BIC     Lik  Chisq Df Pr(&gt;Chisq)</span></span>
+<span><span class="co">## f_saem_reduced                9 663.74 661.87 -322.87                     </span></span>
+<span><span class="co">## best(f_saem_reduced_multi)    9 663.60 661.72 -322.80 0.1476  0           </span></span>
+<span><span class="co">## f_saem_full                  10 670.35 668.26 -325.17 0.0000  1          1</span></span>
+<span><span class="co">## best(f_saem_full_multi)      10 665.61 663.53 -322.80 4.7372  0</span></span></code></pre>
+<p>The reduced model results in lower AIC and BIC values, so it is clearly preferable. Using multiple starting values gives a large improvement in case of the full model, because it is less well-defined, which impedes convergence. For the reduced model, using multiple starting values only results in a small improvement of the model fit.</p>
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