From 5b1179f0daff9077e1370065f9b9f03a2d0e0450 Mon Sep 17 00:00:00 2001
From: Johannes Ranke <jranke@uni-bremen.de>
Date: Thu, 15 Oct 2020 12:53:23 +0200
Subject: Update online docs for release version

---
 docs/reference/confint.mkinfit.html | 219 ++++++++++++++++++++----------------
 1 file changed, 124 insertions(+), 95 deletions(-)

(limited to 'docs/reference/confint.mkinfit.html')

diff --git a/docs/reference/confint.mkinfit.html b/docs/reference/confint.mkinfit.html
index a9080c39..b9e58e8f 100644
--- a/docs/reference/confint.mkinfit.html
+++ b/docs/reference/confint.mkinfit.html
@@ -79,7 +79,7 @@ method of Venzon and Moolgavkar (1988)." />
       </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">0.9.50.2</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.50.3</span>
       </span>
     </div>
 
@@ -116,6 +116,9 @@ method of Venzon and Moolgavkar (1988)." />
     <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>
@@ -124,7 +127,7 @@ method of Venzon and Moolgavkar (1988)." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -143,7 +146,7 @@ method of Venzon and Moolgavkar (1988)." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Confidence intervals for parameters of mkinfit objects</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/confint.mkinfit.R'><code>R/confint.mkinfit.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/confint.mkinfit.R'><code>R/confint.mkinfit.R</code></a></small>
     <div class="hidden name"><code>confint.mkinfit.Rd</code></div>
     </div>
 
@@ -159,19 +162,20 @@ method of Venzon and Moolgavkar (1988).</p>
     </div>
 
     <pre class="usage"><span class='co'># S3 method for mkinfit</span>
-<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(
-  <span class='no'>object</span>,
-  <span class='no'>parm</span>,
-  <span class='kw'>level</span> <span class='kw'>=</span> <span class='fl'>0.95</span>,
-  <span class='kw'>alpha</span> <span class='kw'>=</span> <span class='fl'>1</span> - <span class='no'>level</span>,
-  <span class='no'>cutoff</span>,
-  <span class='kw'>method</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"quadratic"</span>, <span class='st'>"profile"</span>),
-  <span class='kw'>transformed</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>backtransform</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Round.html'>round</a></span>(<span class='fu'>detectCores</span>()/<span class='fl'>2</span>),
-  <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='no'>...</span>
-)</pre>
+<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span>
+  <span class='va'>object</span>,
+  <span class='va'>parm</span>,
+  level <span class='op'>=</span> <span class='fl'>0.95</span>,
+  alpha <span class='op'>=</span> <span class='fl'>1</span> <span class='op'>-</span> <span class='va'>level</span>,
+  <span class='va'>cutoff</span>,
+  method <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='st'>"quadratic"</span>, <span class='st'>"profile"</span><span class='op'>)</span>,
+  transformed <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  backtransform <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  cores <span class='op'>=</span> <span class='fu'>parallel</span><span class='fu'>::</span><span class='fu'><a href='https://rdrr.io/r/parallel/detectCores.html'>detectCores</a></span><span class='op'>(</span><span class='op'>)</span>,
+  rel_tol <span class='op'>=</span> <span class='fl'>0.01</span>,
+  quiet <span class='op'>=</span> <span class='cn'>FALSE</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">
@@ -222,6 +226,12 @@ their confidence intervals?</p></td>
       <th>cores</th>
       <td><p>The number of cores to be used for multicore processing.
 On Windows machines, cores &gt; 1 is currently not supported.</p></td>
+    </tr>
+    <tr>
+      <th>rel_tol</th>
+      <td><p>If the method is 'profile', what should be the accuracy
+of the lower and upper bounds, relative to the estimate obtained from
+the quadratic method?</p></td>
     </tr>
     <tr>
       <th>quiet</th>
@@ -247,69 +257,79 @@ Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37,
 87–94.</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
-    <pre class="examples"><div class='input'><span class='no'>f</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"SFO"</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>)</div><div class='output co'>#&gt;                     2.5%      97.5%
-#&gt; parent_0      71.8242430 93.1600766
-#&gt; k_parent_sink  0.2109541  0.4440528
-#&gt; sigma          1.9778868  7.3681380</div><div class='input'>
+    <pre class="examples"><div class='input'><span class='va'>f</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;                2.5%      97.5%
+#&gt; parent_0 71.8242430 93.1600766
+#&gt; k_parent  0.2109541  0.4440528
+#&gt; sigma     1.9778868  7.3681380</div><div class='input'>
 <span class='co'># \dontrun{</span>
-<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"profile"</span>)</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='output co'>#&gt;                     2.5%      97.5%
-#&gt; parent_0      73.0641834 92.1392181
-#&gt; k_parent_sink  0.2170293  0.4235348
-#&gt; sigma          3.1307772  8.0628314</div><div class='input'>
+<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f</span>, method <span class='op'>=</span> <span class='st'>"profile"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='output co'>#&gt;                2.5%      97.5%
+#&gt; parent_0 73.0641834 92.1392181
+#&gt; k_parent  0.2170293  0.4235348
+#&gt; sigma     3.1307772  8.0628314</div><div class='input'>
 <span class='co'># Set the number of cores for the profiling method for further examples</span>
-<span class='kw'>if</span> (<span class='fu'><a href='https://rdrr.io/r/base/identical.html'>identical</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/Sys.getenv.html'>Sys.getenv</a></span>(<span class='st'>"NOT_CRAN"</span>), <span class='st'>"true"</span>)) {
-  <span class='no'>n_cores</span> <span class='kw'>&lt;-</span> <span class='kw pkg'>parallel</span><span class='kw ns'>::</span><span class='fu'><a href='https://rdrr.io/r/parallel/detectCores.html'>detectCores</a></span>() - <span class='fl'>1</span>
-} <span class='kw'>else</span> {
- <span class='no'>n_cores</span> <span class='kw'>&lt;-</span> <span class='fl'>1</span>
-}
-<span class='kw'>if</span> (<span class='fu'><a href='https://rdrr.io/r/base/Sys.getenv.html'>Sys.getenv</a></span>(<span class='st'>"TRAVIS"</span>) <span class='kw'>!=</span> <span class='st'>""</span>) <span class='no'>n_cores</span> <span class='kw'>=</span> <span class='fl'>1</span>
-<span class='kw'>if</span> (<span class='fu'><a href='https://rdrr.io/r/base/Sys.info.html'>Sys.info</a></span>()[<span class='st'>"sysname"</span>] <span class='kw'>==</span> <span class='st'>"Windows"</span>) <span class='no'>n_cores</span> <span class='kw'>=</span> <span class='fl'>1</span>
-
-<span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>), <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>SFO_SFO.ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>), <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>),
-  <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>f_d_1</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>FOCUS_2006_D</span>, <span class='no'>value</span> <span class='kw'>!=</span> <span class='fl'>0</span>), <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span>(<span class='no'>ci_profile</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_1</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"profile"</span>, <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>))</div><div class='output co'>#&gt;    user  system elapsed 
-#&gt;   3.430   0.000   3.432 </div><div class='input'><span class='co'># Using more cores does not save much time here, as parent_0 takes up most of the time</span>
+<span class='kw'>if</span> <span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/identical.html'>identical</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/Sys.getenv.html'>Sys.getenv</a></span><span class='op'>(</span><span class='st'>"NOT_CRAN"</span><span class='op'>)</span>, <span class='st'>"true"</span><span class='op'>)</span><span class='op'>)</span> <span class='op'>{</span>
+  <span class='va'>n_cores</span> <span class='op'>&lt;-</span> <span class='fu'>parallel</span><span class='fu'>::</span><span class='fu'><a href='https://rdrr.io/r/parallel/detectCores.html'>detectCores</a></span><span class='op'>(</span><span class='op'>)</span> <span class='op'>-</span> <span class='fl'>1</span>
+<span class='op'>}</span> <span class='kw'>else</span> <span class='op'>{</span>
+ <span class='va'>n_cores</span> <span class='op'>&lt;-</span> <span class='fl'>1</span>
+<span class='op'>}</span>
+<span class='kw'>if</span> <span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/Sys.getenv.html'>Sys.getenv</a></span><span class='op'>(</span><span class='st'>"TRAVIS"</span><span class='op'>)</span> <span class='op'>!=</span> <span class='st'>""</span><span class='op'>)</span> <span class='va'>n_cores</span> <span class='op'>=</span> <span class='fl'>1</span>
+<span class='kw'>if</span> <span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/Sys.info.html'>Sys.info</a></span><span class='op'>(</span><span class='op'>)</span><span class='op'>[</span><span class='st'>"sysname"</span><span class='op'>]</span> <span class='op'>==</span> <span class='st'>"Windows"</span><span class='op'>)</span> <span class='va'>n_cores</span> <span class='op'>=</span> <span class='fl'>1</span>
+
+<span class='va'>SFO_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='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>, m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='va'>SFO_SFO.ff</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='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>, m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>,
+  use_of_ff <span class='op'>=</span> <span class='st'>"max"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='va'>f_d_1</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>FOCUS_2006_D</span>, <span class='va'>value</span> <span class='op'>!=</span> <span class='fl'>0</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span><span class='op'>(</span><span class='va'>ci_profile</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_1</span>, method <span class='op'>=</span> <span class='st'>"profile"</span>, cores <span class='op'>=</span> <span class='fl'>1</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;    user  system elapsed 
+#&gt;   3.770   1.035   3.460 </div><div class='input'><span class='co'># Using more cores does not save much time here, as parent_0 takes up most of the time</span>
 <span class='co'># If we additionally exclude parent_0 (the confidence of which is often of</span>
 <span class='co'># minor interest), we get a nice performance improvement from about 50</span>
 <span class='co'># seconds to about 12 seconds if we use at least four cores</span>
-<span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span>(<span class='no'>ci_profile_no_parent_0</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_1</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"profile"</span>,
-  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"k_parent_sink"</span>, <span class='st'>"k_parent_m1"</span>, <span class='st'>"k_m1_sink"</span>, <span class='st'>"sigma"</span>), <span class='kw'>cores</span> <span class='kw'>=</span> <span class='no'>n_cores</span>))</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='output co'>#&gt; <span class='warning'>Warning: scheduled cores 1, 2, 3 encountered errors in user code, all values of the jobs will be affected</span></div><div class='output co'>#&gt; <span class='error'>Error in dimnames(x) &lt;- dn: length of 'dimnames' [2] not equal to array extent</span></div><div class='output co'>#&gt; <span class='message'>Timing stopped at: 0.012 0.042 0.211</span></div><div class='input'><span class='no'>ci_profile</span></div><div class='output co'>#&gt;                        2.5%        97.5%
+<span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span><span class='op'>(</span><span class='va'>ci_profile_no_parent_0</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_1</span>, method <span class='op'>=</span> <span class='st'>"profile"</span>,
+  <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"k_parent_sink"</span>, <span class='st'>"k_parent_m1"</span>, <span class='st'>"k_m1_sink"</span>, <span class='st'>"sigma"</span><span class='op'>)</span>, cores <span class='op'>=</span> <span class='va'>n_cores</span><span class='op'>)</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='output co'>#&gt; <span class='warning'>Warning: scheduled cores 3, 2, 1 encountered errors in user code, all values of the jobs will be affected</span></div><div class='output co'>#&gt; <span class='error'>Error in dimnames(x) &lt;- dn: length of 'dimnames' [2] not equal to array extent</span></div><div class='output co'>#&gt; <span class='message'>Timing stopped at: 0.014 0.027 0.196</span></div><div class='input'><span class='va'>ci_profile</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
 #&gt; parent_0       96.456003640 1.027703e+02
 #&gt; k_parent        0.090911032 1.071578e-01
 #&gt; k_m1            0.003892605 6.702778e-03
 #&gt; f_parent_to_m1  0.471328495 5.611550e-01
-#&gt; sigma           2.535612399 3.985263e+00</div><div class='input'><span class='no'>ci_quadratic_transformed</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_1</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>)
-<span class='no'>ci_quadratic_transformed</span></div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       96.403839476 1.027931e+02
+#&gt; sigma           2.535612399 3.985263e+00</div><div class='input'><span class='va'>ci_quadratic_transformed</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_1</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span><span class='op'>)</span>
+<span class='va'>ci_quadratic_transformed</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       96.403839460 1.027931e+02
 #&gt; k_parent        0.090823790 1.072543e-01
 #&gt; k_m1            0.004012216 6.897547e-03
 #&gt; f_parent_to_m1  0.469118713 5.595960e-01
-#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='no'>ci_quadratic_untransformed</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_1</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>, <span class='kw'>transformed</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)
-<span class='no'>ci_quadratic_untransformed</span></div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       96.403839429 1.027931e+02
+#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='va'>ci_quadratic_untransformed</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_1</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span>, transformed <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
+<span class='va'>ci_quadratic_untransformed</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       96.403839413 1.027931e+02
 #&gt; k_parent        0.090491931 1.069035e-01
 #&gt; k_m1            0.003835483 6.685819e-03
-#&gt; f_parent_to_m1  0.469113364 5.598386e-01
+#&gt; f_parent_to_m1  0.469113365 5.598386e-01
 #&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='co'># Against the expectation based on Bates and Watts (1988), the confidence</span>
 <span class='co'># intervals based on the internal parameter transformation are less</span>
 <span class='co'># congruent with the likelihood based intervals. Note the superiority of the</span>
 <span class='co'># interval based on the untransformed fit for k_m1_sink</span>
-<span class='no'>rel_diffs_transformed</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span>((<span class='no'>ci_quadratic_transformed</span> - <span class='no'>ci_profile</span>)/<span class='no'>ci_profile</span>)
-<span class='no'>rel_diffs_untransformed</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span>((<span class='no'>ci_quadratic_untransformed</span> - <span class='no'>ci_profile</span>)/<span class='no'>ci_profile</span>)
-<span class='no'>rel_diffs_transformed</span> <span class='kw'>&lt;</span> <span class='no'>rel_diffs_untransformed</span></div><div class='output co'>#&gt;                 2.5% 97.5%
+<span class='va'>rel_diffs_transformed</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span><span class='op'>(</span><span class='op'>(</span><span class='va'>ci_quadratic_transformed</span> <span class='op'>-</span> <span class='va'>ci_profile</span><span class='op'>)</span><span class='op'>/</span><span class='va'>ci_profile</span><span class='op'>)</span>
+<span class='va'>rel_diffs_untransformed</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span><span class='op'>(</span><span class='op'>(</span><span class='va'>ci_quadratic_untransformed</span> <span class='op'>-</span> <span class='va'>ci_profile</span><span class='op'>)</span><span class='op'>/</span><span class='va'>ci_profile</span><span class='op'>)</span>
+<span class='va'>rel_diffs_transformed</span> <span class='op'>&lt;</span> <span class='va'>rel_diffs_untransformed</span>
+</div><div class='output co'>#&gt;                 2.5% 97.5%
 #&gt; parent_0        TRUE  TRUE
 #&gt; k_parent        TRUE  TRUE
 #&gt; k_m1           FALSE FALSE
 #&gt; f_parent_to_m1  TRUE FALSE
-#&gt; sigma          FALSE  TRUE</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/Round.html'>signif</a></span>(<span class='no'>rel_diffs_transformed</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;                    2.5%    97.5%
+#&gt; sigma          FALSE FALSE</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/Round.html'>signif</a></span><span class='op'>(</span><span class='va'>rel_diffs_transformed</span>, <span class='fl'>3</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;                    2.5%    97.5%
 #&gt; parent_0       0.000541 0.000222
 #&gt; k_parent       0.000960 0.000900
 #&gt; k_m1           0.030700 0.029100
 #&gt; f_parent_to_m1 0.004690 0.002780
-#&gt; sigma          0.055000 0.032700</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/Round.html'>signif</a></span>(<span class='no'>rel_diffs_untransformed</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;                    2.5%    97.5%
+#&gt; sigma          0.055000 0.032700</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/Round.html'>signif</a></span><span class='op'>(</span><span class='va'>rel_diffs_untransformed</span>, <span class='fl'>3</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;                    2.5%    97.5%
 #&gt; parent_0       0.000541 0.000222
 #&gt; k_parent       0.004610 0.002370
 #&gt; k_m1           0.014700 0.002530
@@ -317,67 +337,76 @@ Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37,
 #&gt; sigma          0.055000 0.032700</div><div class='input'>
 
 <span class='co'># Investigate a case with formation fractions</span>
-<span class='no'>f_d_2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO.ff</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>FOCUS_2006_D</span>, <span class='no'>value</span> <span class='kw'>!=</span> <span class='fl'>0</span>), <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>ci_profile_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_2</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"profile"</span>, <span class='kw'>cores</span> <span class='kw'>=</span> <span class='no'>n_cores</span>)</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='input'><span class='no'>ci_profile_ff</span></div><div class='output co'>#&gt;                        2.5%        97.5%
+<span class='va'>f_d_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>SFO_SFO.ff</span>, <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>FOCUS_2006_D</span>, <span class='va'>value</span> <span class='op'>!=</span> <span class='fl'>0</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='input'><span class='va'>ci_profile_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_2</span>, method <span class='op'>=</span> <span class='st'>"profile"</span>, cores <span class='op'>=</span> <span class='va'>n_cores</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='message'>Profiling the likelihood</span></div><div class='input'><span class='va'>ci_profile_ff</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
 #&gt; parent_0       96.456003640 1.027703e+02
 #&gt; k_parent        0.090911032 1.071578e-01
 #&gt; k_m1            0.003892605 6.702778e-03
 #&gt; f_parent_to_m1  0.471328495 5.611550e-01
-#&gt; sigma           2.535612399 3.985263e+00</div><div class='input'><span class='no'>ci_quadratic_transformed_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_2</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>)
-<span class='no'>ci_quadratic_transformed_ff</span></div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       96.403839476 1.027931e+02
+#&gt; sigma           2.535612399 3.985263e+00</div><div class='input'><span class='va'>ci_quadratic_transformed_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_2</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span><span class='op'>)</span>
+<span class='va'>ci_quadratic_transformed_ff</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       96.403839460 1.027931e+02
 #&gt; k_parent        0.090823790 1.072543e-01
 #&gt; k_m1            0.004012216 6.897547e-03
 #&gt; f_parent_to_m1  0.469118713 5.595960e-01
-#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='no'>ci_quadratic_untransformed_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_d_2</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>, <span class='kw'>transformed</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)
-<span class='no'>ci_quadratic_untransformed_ff</span></div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       96.403839429 1.027931e+02
+#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='va'>ci_quadratic_untransformed_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_d_2</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span>, transformed <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
+<span class='va'>ci_quadratic_untransformed_ff</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       96.403839413 1.027931e+02
 #&gt; k_parent        0.090491931 1.069035e-01
 #&gt; k_m1            0.003835483 6.685819e-03
-#&gt; f_parent_to_m1  0.469113364 5.598386e-01
-#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='no'>rel_diffs_transformed_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span>((<span class='no'>ci_quadratic_transformed_ff</span> - <span class='no'>ci_profile_ff</span>)/<span class='no'>ci_profile_ff</span>)
-<span class='no'>rel_diffs_untransformed_ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span>((<span class='no'>ci_quadratic_untransformed_ff</span> - <span class='no'>ci_profile_ff</span>)/<span class='no'>ci_profile_ff</span>)
+#&gt; f_parent_to_m1  0.469113365 5.598386e-01
+#&gt; sigma           2.396089689 3.854918e+00</div><div class='input'><span class='va'>rel_diffs_transformed_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span><span class='op'>(</span><span class='op'>(</span><span class='va'>ci_quadratic_transformed_ff</span> <span class='op'>-</span> <span class='va'>ci_profile_ff</span><span class='op'>)</span><span class='op'>/</span><span class='va'>ci_profile_ff</span><span class='op'>)</span>
+<span class='va'>rel_diffs_untransformed_ff</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>abs</a></span><span class='op'>(</span><span class='op'>(</span><span class='va'>ci_quadratic_untransformed_ff</span> <span class='op'>-</span> <span class='va'>ci_profile_ff</span><span class='op'>)</span><span class='op'>/</span><span class='va'>ci_profile_ff</span><span class='op'>)</span>
 <span class='co'># While the confidence interval for the parent rate constant is closer to</span>
 <span class='co'># the profile based interval when using the internal parameter</span>
 <span class='co'># transformation, the interval for the metabolite rate constant is 'better</span>
 <span class='co'># without internal parameter transformation.</span>
-<span class='no'>rel_diffs_transformed_ff</span> <span class='kw'>&lt;</span> <span class='no'>rel_diffs_untransformed_ff</span></div><div class='output co'>#&gt;                 2.5% 97.5%
+<span class='va'>rel_diffs_transformed_ff</span> <span class='op'>&lt;</span> <span class='va'>rel_diffs_untransformed_ff</span>
+</div><div class='output co'>#&gt;                 2.5% 97.5%
 #&gt; parent_0        TRUE  TRUE
 #&gt; k_parent        TRUE  TRUE
 #&gt; k_m1           FALSE FALSE
 #&gt; f_parent_to_m1  TRUE FALSE
-#&gt; sigma          FALSE  TRUE</div><div class='input'><span class='no'>rel_diffs_transformed_ff</span></div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       0.0005408078 0.0002217796
+#&gt; sigma          FALSE FALSE</div><div class='input'><span class='va'>rel_diffs_transformed_ff</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       0.0005408080 0.0002217794
 #&gt; k_parent       0.0009596417 0.0009003876
-#&gt; k_m1           0.0307277372 0.0290579184
-#&gt; f_parent_to_m1 0.0046884131 0.0027782558
-#&gt; sigma          0.0550252516 0.0327066836</div><div class='input'><span class='no'>rel_diffs_untransformed_ff</span></div><div class='output co'>#&gt;                        2.5%       97.5%
-#&gt; parent_0       0.0005408083 0.000221780
-#&gt; k_parent       0.0046100096 0.002373023
-#&gt; k_m1           0.0146746467 0.002530101
-#&gt; f_parent_to_m1 0.0046997600 0.002346022
-#&gt; sigma          0.0550252516 0.032706684</div><div class='input'>
+#&gt; k_m1           0.0307277370 0.0290579182
+#&gt; f_parent_to_m1 0.0046884130 0.0027782556
+#&gt; sigma          0.0550252516 0.0327066836</div><div class='input'><span class='va'>rel_diffs_untransformed_ff</span>
+</div><div class='output co'>#&gt;                        2.5%        97.5%
+#&gt; parent_0       0.0005408085 0.0002217799
+#&gt; k_parent       0.0046100096 0.0023730229
+#&gt; k_m1           0.0146746469 0.0025301011
+#&gt; f_parent_to_m1 0.0046997599 0.0023460223
+#&gt; sigma          0.0550252516 0.0327066836</div><div class='input'>
 <span class='co'># The profiling for the following fit does not finish in a reasonable time,</span>
 <span class='co'># therefore we use the quadratic approximation</span>
-<span class='no'>m_synth_DFOP_par</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"DFOP"</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>)),
-  <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>),
-  <span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>),
-  <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='no'>DFOP_par_c</span> <span class='kw'>&lt;-</span> <span class='no'>synthetic_data_for_UBA_2014</span><span class='kw'>[[</span><span class='fl'>12</span>]]$<span class='no'>data</span>
-<span class='no'>f_tc_2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>m_synth_DFOP_par</span>, <span class='no'>DFOP_par_c</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>,
-  <span class='kw'>error_model_algorithm</span> <span class='kw'>=</span> <span class='st'>"direct"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</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='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_tc_2</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>)</div><div class='output co'>#&gt;                        2.5%        97.5%
-#&gt; parent_0       95.654015524 105.79279749
-#&gt; k_M1            0.037723773   0.04447598
-#&gt; k_M2            0.008586438   0.01078076
-#&gt; f_parent_to_M1  0.230403596   0.61953014
-#&gt; f_parent_to_M2  0.162909765   0.38019017
-#&gt; k1              0.275434628   0.33331386
-#&gt; k2              0.018602188   0.02249211
-#&gt; g               0.675149759   0.73520889
-#&gt; sigma_low       0.251416929   0.84272023
-#&gt; rsd_high        0.040371818   0.07666540</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span>(<span class='no'>f_tc_2</span>, <span class='st'>"parent_0"</span>, <span class='kw'>method</span> <span class='kw'>=</span> <span class='st'>"quadratic"</span>)</div><div class='output co'>#&gt;              2.5%    97.5%
-#&gt; parent_0 95.65402 105.7928</div><div class='input'># }
+<span class='va'>m_synth_DFOP_par</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='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"M1"</span>, <span class='st'>"M2"</span><span class='op'>)</span><span class='op'>)</span>,
+  M1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>,
+  M2 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>,
+  use_of_ff <span class='op'>=</span> <span class='st'>"max"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='va'>DFOP_par_c</span> <span class='op'>&lt;-</span> <span class='va'>synthetic_data_for_UBA_2014</span><span class='op'>[[</span><span class='fl'>12</span><span class='op'>]</span><span class='op'>]</span><span class='op'>$</span><span class='va'>data</span>
+<span class='va'>f_tc_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>m_synth_DFOP_par</span>, <span class='va'>DFOP_par_c</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>,
+  error_model_algorithm <span class='op'>=</span> <span class='st'>"direct"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_tc_2</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;                       2.5%        97.5%
+#&gt; parent_0       94.59613833 106.19939215
+#&gt; k_M1            0.03760542   0.04490759
+#&gt; k_M2            0.00856874   0.01087675
+#&gt; f_parent_to_M1  0.02146166   0.62023888
+#&gt; f_parent_to_M2  0.01516502   0.37975343
+#&gt; k1              0.27389751   0.33388078
+#&gt; k2              0.01861456   0.02250379
+#&gt; g               0.67194349   0.73583256
+#&gt; sigma_low       0.25128383   0.83992146
+#&gt; rsd_high        0.04041100   0.07662001</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/stats/confint.html'>confint</a></span><span class='op'>(</span><span class='va'>f_tc_2</span>, <span class='st'>"parent_0"</span>, method <span class='op'>=</span> <span class='st'>"quadratic"</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;              2.5%    97.5%
+#&gt; parent_0 94.59614 106.1994</div><div class='input'><span class='co'># }</span>
 </div></pre>
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -394,7 +423,7 @@ Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37,
 </div>
 
 <div class="pkgdown">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
 </div>
 
       </footer>
-- 
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