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diff --git a/docs/dev/reference/confint.mkinfit.html b/docs/dev/reference/confint.mkinfit.html
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-<meta property="og:description" content="The default method 'quadratic' is based on the quadratic approximation of
+<!-- 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>Confidence intervals for parameters of mkinfit objects — confint.mkinfit • 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" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Confidence intervals for parameters of mkinfit objects — confint.mkinfit"><meta property="og:description" content="The default method 'quadratic' is based on the quadratic approximation of
the curvature of the likelihood function at the maximum likelihood parameter
estimates.
The alternative method 'profile' is based on the profile likelihood for each
parameter. The 'profile' method uses two nested optimisations and can take a
very long time, even if parallelized by specifying 'cores' on unixoid
platforms. The speed of the method could likely be improved by using the
-method of Venzon and Moolgavkar (1988)." />
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@@ -79,23 +24,21 @@ method of Venzon and Moolgavkar (1988)." />
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@@ -105,48 +48,50 @@ method of Venzon and Moolgavkar (1988)." />
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</li>
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- <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
+ <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/multistart.html">Short demo of the multistart method</a>
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+ <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
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<div class="page-header">
<h1>Confidence intervals for parameters of mkinfit objects</h1>
- <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>
+ <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/confint.mkinfit.R" class="external-link"><code>R/confint.mkinfit.R</code></a></small>
<div class="hidden name"><code>confint.mkinfit.Rd</code></div>
</div>
@@ -161,279 +106,301 @@ platforms. The speed of the method could likely be improved by using the
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='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">
- <colgroup><col class="name" /><col class="desc" /></colgroup>
- <tr>
- <th>object</th>
- <td><p>An <code><a href='mkinfit.html'>mkinfit</a></code> object</p></td>
- </tr>
- <tr>
- <th>parm</th>
- <td><p>A vector of names of the parameters which are to be given
-confidence intervals. If missing, all parameters are considered.</p></td>
- </tr>
- <tr>
- <th>level</th>
- <td><p>The confidence level required</p></td>
- </tr>
- <tr>
- <th>alpha</th>
- <td><p>The allowed error probability, overrides 'level' if specified.</p></td>
- </tr>
- <tr>
- <th>cutoff</th>
- <td><p>Possibility to specify an alternative cutoff for the difference
+ <div id="ref-usage">
+ <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for mkinfit</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/stats/confint.html" class="external-link">confint</a></span><span class="op">(</span></span>
+<span> <span class="va">object</span>,</span>
+<span> <span class="va">parm</span>,</span>
+<span> level <span class="op">=</span> <span class="fl">0.95</span>,</span>
+<span> alpha <span class="op">=</span> <span class="fl">1</span> <span class="op">-</span> <span class="va">level</span>,</span>
+<span> <span class="va">cutoff</span>,</span>
+<span> method <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">"quadratic"</span>, <span class="st">"profile"</span><span class="op">)</span>,</span>
+<span> transformed <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span> backtransform <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<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" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span>,</span>
+<span> rel_tol <span class="op">=</span> <span class="fl">0.01</span>,</span>
+<span> quiet <span class="op">=</span> <span class="cn">FALSE</span>,</span>
+<span> <span class="va">...</span></span>
+<span><span class="op">)</span></span></code></pre></div>
+ </div>
+
+ <div id="arguments">
+ <h2>Arguments</h2>
+ <dl><dt>object</dt>
+<dd><p>An <code><a href="mkinfit.html">mkinfit</a></code> object</p></dd>
+
+
+<dt>parm</dt>
+<dd><p>A vector of names of the parameters which are to be given
+confidence intervals. If missing, all parameters are considered.</p></dd>
+
+
+<dt>level</dt>
+<dd><p>The confidence level required</p></dd>
+
+
+<dt>alpha</dt>
+<dd><p>The allowed error probability, overrides 'level' if specified.</p></dd>
+
+
+<dt>cutoff</dt>
+<dd><p>Possibility to specify an alternative cutoff for the difference
in the log-likelihoods at the confidence boundary. Specifying an explicit
-cutoff value overrides arguments 'level' and 'alpha'</p></td>
- </tr>
- <tr>
- <th>method</th>
- <td><p>The 'quadratic' method approximates the likelihood function at
+cutoff value overrides arguments 'level' and 'alpha'</p></dd>
+
+
+<dt>method</dt>
+<dd><p>The 'quadratic' method approximates the likelihood function at
the optimised parameters using the second term of the Taylor expansion,
using a second derivative (hessian) contained in the object.
The 'profile' method searches the parameter space for the
-cutoff of the confidence intervals by means of a likelihood ratio test.</p></td>
- </tr>
- <tr>
- <th>transformed</th>
- <td><p>If the quadratic approximation is used, should it be
-applied to the likelihood based on the transformed parameters?</p></td>
- </tr>
- <tr>
- <th>backtransform</th>
- <td><p>If we approximate the likelihood in terms of the
+cutoff of the confidence intervals by means of a likelihood ratio test.</p></dd>
+
+
+<dt>transformed</dt>
+<dd><p>If the quadratic approximation is used, should it be
+applied to the likelihood based on the transformed parameters?</p></dd>
+
+
+<dt>backtransform</dt>
+<dd><p>If we approximate the likelihood in terms of the
transformed parameters, should we backtransform the parameters with
-their confidence intervals?</p></td>
- </tr>
- <tr>
- <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
+their confidence intervals?</p></dd>
+
+
+<dt>cores</dt>
+<dd><p>The number of cores to be used for multicore processing.
+On Windows machines, cores &gt; 1 is currently not supported.</p></dd>
+
+
+<dt>rel_tol</dt>
+<dd><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>
- <td><p>Should we suppress the message "Profiling the likelihood"</p></td>
- </tr>
- <tr>
- <th>...</th>
- <td><p>Not used</p></td>
- </tr>
- </table>
-
- <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
-
- <p>A matrix with columns giving lower and upper confidence limits for
-each parameter.</p>
- <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
+the quadratic method?</p></dd>
+
+
+<dt>quiet</dt>
+<dd><p>Should we suppress the message "Profiling the likelihood"</p></dd>
+
+<dt>...</dt>
+<dd><p>Not used</p></dd>
+
+</dl></div>
+ <div id="value">
+ <h2>Value</h2>
+
+
+<p>A matrix with columns giving lower and upper confidence limits for
+each parameter.</p>
+ </div>
+ <div id="references">
+ <h2>References</h2>
<p>Bates DM and Watts GW (1988) Nonlinear regression analysis &amp; its applications</p>
<p>Pawitan Y (2013) In all likelihood - Statistical modelling and
inference using likelihood. Clarendon Press, Oxford.</p>
<p>Venzon DJ and Moolgavkar SH (1988) A Method for Computing
Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37,
87–94.</p>
+ </div>
- <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
- <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='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='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='mkinmod.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='mkinmod.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'>"min"</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='mkinmod.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='mkinmod.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>
-<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; 4.295 1.008 3.959 </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 if we use at least 4 cores</span>
-<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; user system elapsed
-#&gt; 1.451 0.126 0.923 </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_sink 0.040762501 5.549764e-02
-#&gt; k_parent_m1 0.046786482 5.500879e-02
-#&gt; k_m1_sink 0.003892605 6.702778e-03
-#&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 96.403841640 1.027931e+02
-#&gt; k_parent_sink 0.041033378 5.596269e-02
-#&gt; k_parent_m1 0.046777902 5.511931e-02
-#&gt; k_m1_sink 0.004012217 6.897547e-03
-#&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 96.403841645 102.79312449
-#&gt; k_parent_sink 0.040485331 0.05535491
-#&gt; k_parent_m1 0.046611582 0.05494364
-#&gt; k_m1_sink 0.003835483 0.00668582
-#&gt; sigma 2.396089689 3.85491806</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='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 FALSE FALSE
-#&gt; k_parent_sink TRUE FALSE
-#&gt; k_parent_m1 TRUE FALSE
-#&gt; k_m1_sink FALSE FALSE
-#&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_sink 0.006650 0.008380
-#&gt; k_parent_m1 0.000183 0.002010
-#&gt; k_m1_sink 0.030700 0.029100
-#&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_sink 0.006800 0.002570
-#&gt; k_parent_m1 0.003740 0.001180
-#&gt; k_m1_sink 0.014700 0.002530
-#&gt; sigma 0.055000 0.032700</div><div class='input'>
-
-<span class='co'># Investigate a case with formation fractions</span>
-<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>
-<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 0.003892606 6.702775e-03
-#&gt; f_parent_to_m1 0.471328495 5.611550e-01
-#&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 96.403833578 102.79311649
-#&gt; k_parent 0.090823771 0.10725430
-#&gt; k_m1 0.004012219 0.00689755
-#&gt; f_parent_to_m1 0.469118824 0.55959615
-#&gt; sigma 2.396089689 3.85491806</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 96.403833583 1.027931e+02
-#&gt; k_parent 0.090491913 1.069035e-01
-#&gt; k_m1 0.003835485 6.685823e-03
-#&gt; f_parent_to_m1 0.469113477 5.598387e-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='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 FALSE FALSE
-#&gt; k_parent TRUE TRUE
-#&gt; k_m1 FALSE FALSE
-#&gt; f_parent_to_m1 TRUE FALSE
-#&gt; sigma TRUE 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 0.0005408690 0.0002217233
-#&gt; k_parent 0.0009598532 0.0009001864
-#&gt; k_m1 0.0307283041 0.0290588361
-#&gt; f_parent_to_m1 0.0046881769 0.0027780063
-#&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 0.0005408689 0.0002217232
-#&gt; k_parent 0.0046102156 0.0023732281
-#&gt; k_m1 0.0146740690 0.0025291820
-#&gt; f_parent_to_m1 0.0046995211 0.0023457712
-#&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='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='mkinmod.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='mkinmod.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='mkinmod.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 94.596039609 106.19954892
-#&gt; k_M1 0.037605368 0.04490762
-#&gt; k_M2 0.008568731 0.01087676
-#&gt; f_parent_to_M1 0.021462489 0.62023882
-#&gt; f_parent_to_M2 0.015165617 0.37975348
-#&gt; k1 0.273897348 0.33388101
-#&gt; k2 0.018614554 0.02250378
-#&gt; g 0.671943411 0.73583305
-#&gt; sigma_low 0.251283495 0.83992077
-#&gt; rsd_high 0.040411024 0.07662008</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 94.59604 106.1995</div><div class='input'><span class='co'># }</span>
-</div></pre>
+ <div id="ref-examples">
+ <h2>Examples</h2>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><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></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/stats/confint.html" class="external-link">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></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 71.8242430 93.1600766</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent 0.2109541 0.4440528</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 1.9778868 7.3681380</span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/stats/confint.html" class="external-link">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></span></span>
+<span class="r-msg co"><span class="r-pr">#&gt;</span> Profiling the likelihood</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 73.0641834 92.1392181</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent 0.2170293 0.4235348</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 3.1307772 8.0628314</span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># Set the number of cores for the profiling method for further examples</span></span></span>
+<span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/identical.html" class="external-link">identical</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html" class="external-link">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></span>
+<span class="r-in"><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" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span> <span class="op">-</span> <span class="fl">1</span></span></span>
+<span class="r-in"><span><span class="op">}</span> <span class="kw">else</span> <span class="op">{</span></span></span>
+<span class="r-in"><span> <span class="va">n_cores</span> <span class="op">&lt;-</span> <span class="fl">1</span></span></span>
+<span class="r-in"><span><span class="op">}</span></span></span>
+<span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.getenv.html" class="external-link">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></span>
+<span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">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></span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><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="mkinmod.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="mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span></span>
+<span class="r-in"><span> use_of_ff <span class="op">=</span> <span class="st">"min"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
+<span class="r-in"><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="mkinmod.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="mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span></span>
+<span class="r-in"><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></span>
+<span class="r-in"><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" class="external-link">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></span></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">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" class="external-link">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></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> user system elapsed </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 3.811 0.004 3.815 </span>
+<span class="r-in"><span><span class="co"># Using more cores does not save much time here, as parent_0 takes up most of the time</span></span></span>
+<span class="r-in"><span><span class="co"># If we additionally exclude parent_0 (the confidence of which is often of</span></span></span>
+<span class="r-in"><span><span class="co"># minor interest), we get a nice performance improvement if we use at least 4 cores</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">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" class="external-link">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></span>
+<span class="r-in"><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">"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></span></span>
+<span class="r-msg co"><span class="r-pr">#&gt;</span> Profiling the likelihood</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> user system elapsed </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.313 0.004 2.318 </span>
+<span class="r-in"><span><span class="va">ci_profile</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 96.456003640 1.027703e+02</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_sink 0.040762501 5.549764e-02</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_m1 0.046786482 5.500879e-02</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1_sink 0.003892605 6.702778e-03</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 2.535612399 3.985263e+00</span>
+<span class="r-in"><span><span class="va">ci_quadratic_transformed</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/confint.html" class="external-link">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></span>
+<span class="r-in"><span><span class="va">ci_quadratic_transformed</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 96.403841640 1.027931e+02</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_sink 0.041033378 5.596269e-02</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_m1 0.046777902 5.511931e-02</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1_sink 0.004012217 6.897547e-03</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 2.396089689 3.854918e+00</span>
+<span class="r-in"><span><span class="va">ci_quadratic_untransformed</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/confint.html" class="external-link">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></span>
+<span class="r-in"><span><span class="va">ci_quadratic_untransformed</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 96.403841645 102.79312449</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_sink 0.040485331 0.05535491</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_m1 0.046611582 0.05494364</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1_sink 0.003835483 0.00668582</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 2.396089689 3.85491806</span>
+<span class="r-in"><span><span class="co"># Against the expectation based on Bates and Watts (1988), the confidence</span></span></span>
+<span class="r-in"><span><span class="co"># intervals based on the internal parameter transformation are less</span></span></span>
+<span class="r-in"><span><span class="co"># congruent with the likelihood based intervals. Note the superiority of the</span></span></span>
+<span class="r-in"><span><span class="co"># interval based on the untransformed fit for k_m1_sink</span></span></span>
+<span class="r-in"><span><span class="va">rel_diffs_transformed</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">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></span>
+<span class="r-in"><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" class="external-link">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></span>
+<span class="r-in"><span><span class="va">rel_diffs_transformed</span> <span class="op">&lt;</span> <span class="va">rel_diffs_untransformed</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 FALSE FALSE</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_sink TRUE FALSE</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_m1 TRUE FALSE</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1_sink FALSE FALSE</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma FALSE FALSE</span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">signif</a></span><span class="op">(</span><span class="va">rel_diffs_transformed</span>, <span class="fl">3</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 0.000541 0.000222</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_sink 0.006650 0.008380</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_m1 0.000183 0.002010</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1_sink 0.030700 0.029100</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 0.055000 0.032700</span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">signif</a></span><span class="op">(</span><span class="va">rel_diffs_untransformed</span>, <span class="fl">3</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 0.000541 0.000222</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_sink 0.006800 0.002570</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent_m1 0.003740 0.001180</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1_sink 0.014700 0.002530</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 0.055000 0.032700</span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># Investigate a case with formation fractions</span></span></span>
+<span class="r-in"><span><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" class="external-link">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></span></span>
+<span class="r-in"><span><span class="va">ci_profile_ff</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/confint.html" class="external-link">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></span></span>
+<span class="r-msg co"><span class="r-pr">#&gt;</span> Profiling the likelihood</span>
+<span class="r-in"><span><span class="va">ci_profile_ff</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 96.456003640 1.027703e+02</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent 0.090911032 1.071578e-01</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1 0.003892606 6.702775e-03</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> f_parent_to_m1 0.471328495 5.611550e-01</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 2.535612399 3.985263e+00</span>
+<span class="r-in"><span><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" class="external-link">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></span>
+<span class="r-in"><span><span class="va">ci_quadratic_transformed_ff</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 96.403833578 102.79311649</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent 0.090823771 0.10725430</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1 0.004012219 0.00689755</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> f_parent_to_m1 0.469118824 0.55959615</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 2.396089689 3.85491806</span>
+<span class="r-in"><span><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" class="external-link">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></span>
+<span class="r-in"><span><span class="va">ci_quadratic_untransformed_ff</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 96.403833583 1.027931e+02</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent 0.090491913 1.069035e-01</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1 0.003835485 6.685823e-03</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> f_parent_to_m1 0.469113477 5.598387e-01</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 2.396089689 3.854918e+00</span>
+<span class="r-in"><span><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" class="external-link">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></span>
+<span class="r-in"><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" class="external-link">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></span>
+<span class="r-in"><span><span class="co"># While the confidence interval for the parent rate constant is closer to</span></span></span>
+<span class="r-in"><span><span class="co"># the profile based interval when using the internal parameter</span></span></span>
+<span class="r-in"><span><span class="co"># transformation, the interval for the metabolite rate constant is 'better</span></span></span>
+<span class="r-in"><span><span class="co"># without internal parameter transformation.</span></span></span>
+<span class="r-in"><span><span class="va">rel_diffs_transformed_ff</span> <span class="op">&lt;</span> <span class="va">rel_diffs_untransformed_ff</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 FALSE FALSE</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent TRUE TRUE</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1 FALSE FALSE</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> f_parent_to_m1 TRUE FALSE</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma TRUE FALSE</span>
+<span class="r-in"><span><span class="va">rel_diffs_transformed_ff</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 0.0005408690 0.0002217233</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent 0.0009598532 0.0009001864</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1 0.0307283041 0.0290588361</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> f_parent_to_m1 0.0046881769 0.0027780063</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 0.0550252516 0.0327066836</span>
+<span class="r-in"><span><span class="va">rel_diffs_untransformed_ff</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 0.0005408689 0.0002217232</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_parent 0.0046102156 0.0023732281</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_m1 0.0146740690 0.0025291820</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> f_parent_to_m1 0.0046995211 0.0023457712</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma 0.0550252516 0.0327066836</span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># The profiling for the following fit does not finish in a reasonable time,</span></span></span>
+<span class="r-in"><span><span class="co"># therefore we use the quadratic approximation</span></span></span>
+<span class="r-in"><span><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="mkinmod.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" class="external-link">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>,</span></span>
+<span class="r-in"><span> M1 <span class="op">=</span> <span class="fu"><a href="mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span></span>
+<span class="r-in"><span> M2 <span class="op">=</span> <span class="fu"><a href="mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span></span>
+<span class="r-in"><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></span>
+<span class="r-in"><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></span>
+<span class="r-in"><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>,</span></span>
+<span class="r-in"><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></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/stats/confint.html" class="external-link">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></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 94.596039609 106.19954892</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_M1 0.037605368 0.04490762</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k_M2 0.008568731 0.01087676</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> f_parent_to_M1 0.021462489 0.62023882</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> f_parent_to_M2 0.015165617 0.37975348</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k1 0.273897348 0.33388101</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> k2 0.018614554 0.02250378</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> g 0.671943411 0.73583305</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> sigma_low 0.251283495 0.83992077</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> rsd_high 0.040411024 0.07662008</span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/stats/confint.html" class="external-link">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></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2.5% 97.5%</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> parent_0 94.59604 106.1995</span>
+<span class="r-in"><span><span class="co"># }</span></span></span>
+</code></pre></div>
+ </div>
</div>
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