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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)."><!-- 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-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.4</span> - </span> - </div> - - <div id="navbar" class="navbar-collapse collapse"> - <ul class="nav navbar-nav"><li> - <a href="../reference/index.html">Reference</a> -</li> -<li class="dropdown"> - <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" 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 class="divider"> - <li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</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 class="divider"> - <li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li> - <li> - <a href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a> - </li> - <li> - <a href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a> - </li> - <li> - <a href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a> - </li> - <li> - <a href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a> - </li> - <li> - <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> - </li> - <li class="divider"> - <li class="dropdown-header">Performance</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/web_only/benchmarks.html">Benchmark timings for mkin</a> - </li> - <li> - <a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> - </li> - <li class="divider"> - <li class="dropdown-header">Miscellaneous</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> +method of Venzon and Moolgavkar (1988)."><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)."></head><body> + <a href="#main" class="visually-hidden-focusable">Skip to contents</a> + + + <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="default" aria-label="Site navigation"><div class="container"> + + <a class="navbar-brand me-2" href="../index.html">mkin</a> + + <small class="nav-text text-default me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.9</small> + + + <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> + <span class="navbar-toggler-icon"></span> + </button> + + <div id="navbar" class="collapse navbar-collapse ms-3"> + <ul class="navbar-nav me-auto"><li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li> +<li class="nav-item dropdown"> + <button class="nav-link dropdown-toggle" type="button" id="dropdown-articles" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true">Articles</button> + <ul class="dropdown-menu" aria-labelledby="dropdown-articles"><li><a class="dropdown-item" href="../articles/mkin.html">Introduction to mkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6></li> + <li><a class="dropdown-item" href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a></li> + <li><a class="dropdown-item" href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a></li> + <li><a class="dropdown-item" href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with hierarchical models (nonlinear mixed-effects models)</h6></li> + <li><a class="dropdown-item" href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></li> + <li><a class="dropdown-item" href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></li> + <li><a class="dropdown-item" href="../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li> + <li><a class="dropdown-item" href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></li> + <li><a class="dropdown-item" href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a></li> + <li><a class="dropdown-item" href="../articles/web_only/multistart.html">Short demo of the multistart method</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Performance</h6></li> + <li><a class="dropdown-item" href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></li> + <li><a class="dropdown-item" href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a></li> + <li><a class="dropdown-item" href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Miscellaneous</h6></li> + <li><a class="dropdown-item" href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a></li> + <li><a class="dropdown-item" href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a></li> </ul></li> -<li> - 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<div class="ref-description"> + <div class="ref-description section level2"> <p>The default method 'quadratic' is based on the quadratic approximation of the curvature of the likelihood function at the maximum likelihood parameter estimates. @@ -123,8 +85,9 @@ platforms. The speed of the method could likely be improved by using the method of Venzon and Moolgavkar (1988).</p> </div> - <div id="ref-usage"> - <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for mkinfit</span></span> + <div class="section level2"> + <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2> + <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class '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> @@ -141,32 +104,34 @@ method of Venzon and Moolgavkar (1988).</p> <span><span class="op">)</span></span></code></pre></div> </div> - <div id="arguments"> - <h2>Arguments</h2> - <dl><dt>object</dt> + <div class="section level2"> + <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2> + + +<dl><dt id="arg-object">object<a class="anchor" aria-label="anchor" href="#arg-object"></a></dt> <dd><p>An <code><a href="mkinfit.html">mkinfit</a></code> object</p></dd> -<dt>parm</dt> +<dt id="arg-parm">parm<a class="anchor" aria-label="anchor" href="#arg-parm"></a></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> +<dt id="arg-level">level<a class="anchor" aria-label="anchor" href="#arg-level"></a></dt> <dd><p>The confidence level required</p></dd> -<dt>alpha</dt> +<dt id="arg-alpha">alpha<a class="anchor" aria-label="anchor" href="#arg-alpha"></a></dt> <dd><p>The allowed error probability, overrides 'level' if specified.</p></dd> -<dt>cutoff</dt> +<dt id="arg-cutoff">cutoff<a class="anchor" aria-label="anchor" href="#arg-cutoff"></a></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></dd> -<dt>method</dt> +<dt id="arg-method">method<a class="anchor" aria-label="anchor" href="#arg-method"></a></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. @@ -174,45 +139,43 @@ The 'profile' method searches the parameter space for the cutoff of the confidence intervals by means of a likelihood ratio test.</p></dd> -<dt>transformed</dt> +<dt id="arg-transformed">transformed<a class="anchor" aria-label="anchor" href="#arg-transformed"></a></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> +<dt id="arg-backtransform">backtransform<a class="anchor" aria-label="anchor" href="#arg-backtransform"></a></dt> <dd><p>If we approximate the likelihood in terms of the transformed parameters, should we backtransform the parameters with their confidence intervals?</p></dd> -<dt>cores</dt> +<dt id="arg-cores">cores<a class="anchor" aria-label="anchor" href="#arg-cores"></a></dt> <dd><p>The number of cores to be used for multicore processing. On Windows machines, cores > 1 is currently not supported.</p></dd> -<dt>rel_tol</dt> +<dt id="arg-rel-tol">rel_tol<a class="anchor" aria-label="anchor" href="#arg-rel-tol"></a></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></dd> -<dt>quiet</dt> +<dt id="arg-quiet">quiet<a class="anchor" aria-label="anchor" href="#arg-quiet"></a></dt> <dd><p>Should we suppress the message "Profiling the likelihood"</p></dd> -<dt>...</dt> +<dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></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 + <div class="section level2"> + <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2> + <p>A matrix with columns giving lower and upper confidence limits for each parameter.</p> </div> - <div id="references"> - <h2>References</h2> + <div class="section level2"> + <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a></h2> <p>Bates DM and Watts GW (1988) Nonlinear regression analysis & its applications</p> <p>Pawitan Y (2013) In all likelihood - Statistical modelling and inference using likelihood. Clarendon Press, Oxford.</p> @@ -221,8 +184,8 @@ Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37, 87–94.</p> </div> - <div id="ref-examples"> - <h2>Examples</h2> + <div class="section level2"> + <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2> <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="va">f</span> <span class="op"><-</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">#></span> 2.5% 97.5%</span> @@ -254,7 +217,7 @@ Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37, <span class="r-in"><span><span class="va">f_d_1</span> <span class="op"><-</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"><-</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">#></span> user system elapsed </span> -<span class="r-out co"><span class="r-pr">#></span> 1.086 0.000 1.086 </span> +<span class="r-out co"><span class="r-pr">#></span> 1.206 0.000 1.206 </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> @@ -262,7 +225,7 @@ Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37, <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">#></span> Profiling the likelihood</span> <span class="r-out co"><span class="r-pr">#></span> user system elapsed </span> -<span class="r-out co"><span class="r-pr">#></span> 0.396 0.065 0.263 </span> +<span class="r-out co"><span class="r-pr">#></span> 0.406 0.172 0.317 </span> <span class="r-in"><span><span class="va">ci_profile</span></span></span> <span class="r-out co"><span class="r-pr">#></span> 2.5% 97.5%</span> <span class="r-out co"><span class="r-pr">#></span> parent_0 96.456003640 1.027703e+02</span> @@ -397,27 +360,23 @@ Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37, <span class="r-in"><span><span class="co"># }</span></span></span> </code></pre></div> </div> - 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