aboutsummaryrefslogtreecommitdiff
path: root/docs/dev/reference/confint.mkinfit.html
diff options
context:
space:
mode:
authorJohannes Ranke <jranke@uni-bremen.de>2020-05-27 06:06:08 +0200
committerJohannes Ranke <jranke@uni-bremen.de>2020-05-27 06:06:08 +0200
commita77a10ea6c607346778ba0700b3b66ac393101a2 (patch)
treee91f627fba0580ef237ecbc8f24d6294a59597d3 /docs/dev/reference/confint.mkinfit.html
parent675a733fa2acc08daabb9b8b571c7d658f281f73 (diff)
Create up to date pkgdown docs in development mode
Diffstat (limited to 'docs/dev/reference/confint.mkinfit.html')
-rw-r--r--docs/dev/reference/confint.mkinfit.html419
1 files changed, 419 insertions, 0 deletions
diff --git a/docs/dev/reference/confint.mkinfit.html b/docs/dev/reference/confint.mkinfit.html
new file mode 100644
index 00000000..a03ecea8
--- /dev/null
+++ b/docs/dev/reference/confint.mkinfit.html
@@ -0,0 +1,419 @@
+<!-- Generated by pkgdown: do not edit by hand -->
+<!DOCTYPE html>
+<html lang="en">
+ <head>
+ <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)." />
+
+
+<meta name="robots" content="noindex">
+
+<!-- mathjax -->
+<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script>
+<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script>
+
+<!--[if lt IE 9]>
+<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
+<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
+<![endif]-->
+
+
+
+ </head>
+
+ <body data-spy="scroll" data-target="#toc">
+ <div class="container template-reference-topic">
+ <header>
+ <div class="navbar navbar-default navbar-fixed-top" role="navigation">
+ <div class="container">
+ <div class="navbar-header">
+ <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false">
+ <span class="sr-only">Toggle navigation</span>
+ <span class="icon-bar"></span>
+ <span class="icon-bar"></span>
+ <span class="icon-bar"></span>
+ </button>
+ <span class="navbar-brand">
+ <a class="navbar-link" href="../index.html">mkin</a>
+ <span class="version label label-danger" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.3</span>
+ </span>
+ </div>
+
+ <div id="navbar" class="navbar-collapse collapse">
+ <ul class="nav navbar-nav">
+ <li>
+ <a href="../reference/index.html">Functions and data</a>
+</li>
+<li class="dropdown">
+ <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
+ Articles
+
+ <span class="caret"></span>
+ </a>
+ <ul class="dropdown-menu" role="menu">
+ <li>
+ <a href="../articles/mkin.html">Introduction to mkin</a>
+ </li>
+ <li>
+ <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a>
+ </li>
+ <li>
+ <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
+ </li>
+ <li>
+ <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
+ </li>
+ <li>
+ <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
+ </li>
+ <li>
+ <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
+ </li>
+ <li>
+ <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
+ </li>
+ <li>
+ <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
+ </li>
+ </ul>
+</li>
+<li>
+ <a href="../news/index.html">News</a>
+</li>
+ </ul>
+ <ul class="nav navbar-nav navbar-right">
+ <li>
+ <a href="http://github.com/jranke/mkin/">
+ <span class="fab fa fab fa-github fa-lg"></span>
+
+ </a>
+</li>
+ </ul>
+
+ </div><!--/.nav-collapse -->
+ </div><!--/.container -->
+</div><!--/.navbar -->
+
+
+
+ </header>
+
+<div class="row">
+ <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>
+ <div class="hidden name"><code>confint.mkinfit.Rd</code></div>
+ </div>
+
+ <div class="ref-description">
+ <p>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).</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='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='kw'>rel_tol</span> <span class='kw'>=</span> <span class='fl'>0.01</span>,
+ <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
+ <span class='no'>...</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
+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
+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
+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
+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>
+
+ <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>
+
+ <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'>
+<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='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; 3.707 1.077 3.444 </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 2, 1, 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: 0.011 0.026 0.207</span></div><div class='input'><span class='no'>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; 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; 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='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%
+#&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; 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; parent_0 0.000541 0.000222
+#&gt; k_parent 0.004610 0.002370
+#&gt; k_m1 0.014700 0.002530
+#&gt; f_parent_to_m1 0.004700 0.002350
+#&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%
+#&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; 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; 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>)
+<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%
+#&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; 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'>
+<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'># }
+</div></pre>
+ </div>
+ <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+ <nav id="toc" data-toggle="toc" class="sticky-top">
+ <h2 data-toc-skip>Contents</h2>
+ </nav>
+ </div>
+</div>
+
+
+ <footer>
+ <div class="copyright">
+ <p>Developed by Johannes Ranke.</p>
+</div>
+
+<div class="pkgdown">
+ <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+</div>
+
+ </footer>
+ </div>
+
+
+
+
+ </body>
+</html>
+
+

Contact - Imprint