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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>Fit a kinetic model to data with one or more state variables — 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="Fit a kinetic model to data with one or more state variables — mkinfit"><meta property="og:description" content="This function maximises the likelihood of the observed data using the Port algorithm stats::nlminb(), and the specified initial or fixed parameters and starting values. In each step of the optimisation, the kinetic model is solved using the function mkinpredict(), except @@ -48,28 +7,14 @@ if an analytical solution is implemented, in which case the model is solved using the degradation function in the mkinmod object. The parameters of the selected error model are fitted simultaneously with the degradation model parameters, as both of them are arguments of the -likelihood function." /> - - -<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]> +likelihood function."><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]--> +<![endif]--></head><body data-spy="scroll" data-target="#toc"> + - - - </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"> + <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"> @@ -80,23 +25,21 @@ likelihood function." /> </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">mkin</a> - <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.0.3.9000</span> + <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">1.1.2</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> - <ul class="nav navbar-nav"> - <li> + <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"> + <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> + <ul class="dropdown-menu" role="menu"><li> <a href="../articles/mkin.html">Introduction to mkin</a> </li> <li> @@ -106,6 +49,9 @@ likelihood function." /> <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> + <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/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> </li> <li> @@ -120,91 +66,84 @@ likelihood function." /> <li> <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a> </li> - </ul> -</li> + </ul></li> <li> <a href="../news/index.html">News</a> </li> - </ul> - <ul class="nav navbar-nav navbar-right"> - <li> - <a href="https://github.com/jranke/mkin/"> + </ul><ul class="nav navbar-nav navbar-right"><li> + <a href="https://github.com/jranke/mkin/" class="external-link"> <span class="fab fa-github fa-lg"></span> </a> </li> - </ul> - - </div><!--/.nav-collapse --> + </ul></div><!--/.nav-collapse --> </div><!--/.container --> </div><!--/.navbar --> - </header> - -<div class="row"> + </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header"> <h1>Fit a kinetic model to data with one or more state variables</h1> - <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mkinfit.R'><code>R/mkinfit.R</code></a></small> + <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/mkinfit.R" class="external-link"><code>R/mkinfit.R</code></a></small> <div class="hidden name"><code>mkinfit.Rd</code></div> </div> <div class="ref-description"> <p>This function maximises the likelihood of the observed data using the Port -algorithm <code><a href='https://rdrr.io/r/stats/nlminb.html'>stats::nlminb()</a></code>, and the specified initial or fixed +algorithm <code><a href="https://rdrr.io/r/stats/nlminb.html" class="external-link">stats::nlminb()</a></code>, and the specified initial or fixed parameters and starting values. In each step of the optimisation, the -kinetic model is solved using the function <code><a href='mkinpredict.html'>mkinpredict()</a></code>, except +kinetic model is solved using the function <code><a href="mkinpredict.html">mkinpredict()</a></code>, except if an analytical solution is implemented, in which case the model is solved -using the degradation function in the <a href='mkinmod.html'>mkinmod</a> object. The +using the degradation function in the <a href="mkinmod.html">mkinmod</a> object. The parameters of the selected error model are fitted simultaneously with the degradation model parameters, as both of them are arguments of the likelihood function.</p> </div> - <pre class="usage"><span class='fu'>mkinfit</span><span class='op'>(</span> - <span class='va'>mkinmod</span>, - <span class='va'>observed</span>, - parms.ini <span class='op'>=</span> <span class='st'>"auto"</span>, - state.ini <span class='op'>=</span> <span class='st'>"auto"</span>, - err.ini <span class='op'>=</span> <span class='st'>"auto"</span>, - fixed_parms <span class='op'>=</span> <span class='cn'>NULL</span>, - fixed_initials <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>mkinmod</span><span class='op'>$</span><span class='va'>diffs</span><span class='op'>)</span><span class='op'>[</span><span class='op'>-</span><span class='fl'>1</span><span class='op'>]</span>, - from_max_mean <span class='op'>=</span> <span class='cn'>FALSE</span>, - solution_type <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'>"auto"</span>, <span class='st'>"analytical"</span>, <span class='st'>"eigen"</span>, <span class='st'>"deSolve"</span><span class='op'>)</span>, - method.ode <span class='op'>=</span> <span class='st'>"lsoda"</span>, - use_compiled <span class='op'>=</span> <span class='st'>"auto"</span>, - control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>eval.max <span class='op'>=</span> <span class='fl'>300</span>, iter.max <span class='op'>=</span> <span class='fl'>200</span><span class='op'>)</span>, - transform_rates <span class='op'>=</span> <span class='cn'>TRUE</span>, - transform_fractions <span class='op'>=</span> <span class='cn'>TRUE</span>, - quiet <span class='op'>=</span> <span class='cn'>FALSE</span>, - atol <span class='op'>=</span> <span class='fl'>1e-08</span>, - rtol <span class='op'>=</span> <span class='fl'>1e-10</span>, - error_model <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'>"const"</span>, <span class='st'>"obs"</span>, <span class='st'>"tc"</span><span class='op'>)</span>, - error_model_algorithm <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'>"auto"</span>, <span class='st'>"d_3"</span>, <span class='st'>"direct"</span>, <span class='st'>"twostep"</span>, <span class='st'>"threestep"</span>, - <span class='st'>"fourstep"</span>, <span class='st'>"IRLS"</span>, <span class='st'>"OLS"</span><span class='op'>)</span>, - reweight.tol <span class='op'>=</span> <span class='fl'>1e-08</span>, - reweight.max.iter <span class='op'>=</span> <span class='fl'>10</span>, - trace_parms <span class='op'>=</span> <span class='cn'>FALSE</span>, - test_residuals <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>mkinmod</th> - <td><p>A list of class <a href='mkinmod.html'>mkinmod</a>, containing the kinetic + <div id="ref-usage"> + <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">mkinfit</span><span class="op">(</span></span> +<span> <span class="va">mkinmod</span>,</span> +<span> <span class="va">observed</span>,</span> +<span> parms.ini <span class="op">=</span> <span class="st">"auto"</span>,</span> +<span> state.ini <span class="op">=</span> <span class="st">"auto"</span>,</span> +<span> err.ini <span class="op">=</span> <span class="st">"auto"</span>,</span> +<span> fixed_parms <span class="op">=</span> <span class="cn">NULL</span>,</span> +<span> fixed_initials <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">mkinmod</span><span class="op">$</span><span class="va">diffs</span><span class="op">)</span><span class="op">[</span><span class="op">-</span><span class="fl">1</span><span class="op">]</span>,</span> +<span> from_max_mean <span class="op">=</span> <span class="cn">FALSE</span>,</span> +<span> solution_type <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">"auto"</span>, <span class="st">"analytical"</span>, <span class="st">"eigen"</span>, <span class="st">"deSolve"</span><span class="op">)</span>,</span> +<span> method.ode <span class="op">=</span> <span class="st">"lsoda"</span>,</span> +<span> use_compiled <span class="op">=</span> <span class="st">"auto"</span>,</span> +<span> control <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>eval.max <span class="op">=</span> <span class="fl">300</span>, iter.max <span class="op">=</span> <span class="fl">200</span><span class="op">)</span>,</span> +<span> transform_rates <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> transform_fractions <span class="op">=</span> <span class="cn">TRUE</span>,</span> +<span> quiet <span class="op">=</span> <span class="cn">FALSE</span>,</span> +<span> atol <span class="op">=</span> <span class="fl">1e-08</span>,</span> +<span> rtol <span class="op">=</span> <span class="fl">1e-10</span>,</span> +<span> error_model <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">"const"</span>, <span class="st">"obs"</span>, <span class="st">"tc"</span><span class="op">)</span>,</span> +<span> error_model_algorithm <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">"auto"</span>, <span class="st">"d_3"</span>, <span class="st">"direct"</span>, <span class="st">"twostep"</span>, <span class="st">"threestep"</span>, <span class="st">"fourstep"</span>,</span> +<span> <span class="st">"IRLS"</span>, <span class="st">"OLS"</span><span class="op">)</span>,</span> +<span> reweight.tol <span class="op">=</span> <span class="fl">1e-08</span>,</span> +<span> reweight.max.iter <span class="op">=</span> <span class="fl">10</span>,</span> +<span> trace_parms <span class="op">=</span> <span class="cn">FALSE</span>,</span> +<span> test_residuals <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>mkinmod</dt> +<dd><p>A list of class <a href="mkinmod.html">mkinmod</a>, containing the kinetic model to be fitted to the data, or one of the shorthand names ("SFO", "FOMC", "DFOP", "HS", "SFORB", "IORE"). If a shorthand name is given, a parent only degradation model is generated for the variable with the -highest value in <code>observed</code>.</p></td> - </tr> - <tr> - <th>observed</th> - <td><p>A dataframe with the observed data. The first column called +highest value in <code>observed</code>.</p></dd> + + +<dt>observed</dt> +<dd><p>A dataframe with the observed data. The first column called "name" must contain the name of the observed variable for each data point. The second column must contain the times of observation, named "time". The third column must be named "value" and contain the observed values. @@ -212,11 +151,11 @@ Zero values in the "value" column will be removed, with a warning, in order to avoid problems with fitting the two-component error model. This is not expected to be a problem, because in general, values of zero are not observed in degradation data, because there is a lower limit of -detection.</p></td> - </tr> - <tr> - <th>parms.ini</th> - <td><p>A named vector of initial values for the parameters, +detection.</p></dd> + + +<dt>parms.ini</dt> +<dd><p>A named vector of initial values for the parameters, including parameters to be optimised and potentially also fixed parameters as indicated by <code>fixed_parms</code>. If set to "auto", initial values for rate constants are set to default values. Using parameter names that are @@ -225,113 +164,113 @@ not in the model gives an error.</p> needs. You can use the parameter lists "bparms.ode" from a previously fitted model, which contains the differential equation parameters from this model. This works nicely if the models are nested. An example is -given below.</p></td> - </tr> - <tr> - <th>state.ini</th> - <td><p>A named vector of initial values for the state variables of +given below.</p></dd> + + +<dt>state.ini</dt> +<dd><p>A named vector of initial values for the state variables of the model. In case the observed variables are represented by more than one model variable, the names will differ from the names of the observed -variables (see <code>map</code> component of <a href='mkinmod.html'>mkinmod</a>). The default +variables (see <code>map</code> component of <a href="mkinmod.html">mkinmod</a>). The default is to set the initial value of the first model variable to the mean of the time zero values for the variable with the maximum observed value, and all others to 0. If this variable has no time zero observations, its initial -value is set to 100.</p></td> - </tr> - <tr> - <th>err.ini</th> - <td><p>A named vector of initial values for the error model +value is set to 100.</p></dd> + + +<dt>err.ini</dt> +<dd><p>A named vector of initial values for the error model parameters to be optimised. If set to "auto", initial values are set to default values. Otherwise, inital values for all error model parameters -must be given.</p></td> - </tr> - <tr> - <th>fixed_parms</th> - <td><p>The names of parameters that should not be optimised but +must be given.</p></dd> + + +<dt>fixed_parms</dt> +<dd><p>The names of parameters that should not be optimised but rather kept at the values specified in <code>parms.ini</code>. Alternatively, a named numeric vector of parameters to be fixed, regardless of the values -in parms.ini.</p></td> - </tr> - <tr> - <th>fixed_initials</th> - <td><p>The names of model variables for which the initial +in parms.ini.</p></dd> + + +<dt>fixed_initials</dt> +<dd><p>The names of model variables for which the initial state at time 0 should be excluded from the optimisation. Defaults to all -state variables except for the first one.</p></td> - </tr> - <tr> - <th>from_max_mean</th> - <td><p>If this is set to TRUE, and the model has only one +state variables except for the first one.</p></dd> + + +<dt>from_max_mean</dt> +<dd><p>If this is set to TRUE, and the model has only one observed variable, then data before the time of the maximum observed value (after averaging for each sampling time) are discarded, and this time is subtracted from all remaining time values, so the time of the maximum -observed mean value is the new time zero.</p></td> - </tr> - <tr> - <th>solution_type</th> - <td><p>If set to "eigen", the solution of the system of +observed mean value is the new time zero.</p></dd> + + +<dt>solution_type</dt> +<dd><p>If set to "eigen", the solution of the system of differential equations is based on the spectral decomposition of the coefficient matrix in cases that this is possible. If set to "deSolve", a -numerical <a href='https://rdrr.io/pkg/deSolve/man/ode.html'>ode solver from package deSolve</a> is used. If +numerical <a href="https://rdrr.io/pkg/deSolve/man/ode.html" class="external-link">ode solver from package deSolve</a> is used. If set to "analytical", an analytical solution of the model is used. This is only implemented for relatively simple degradation models. The default is "auto", which uses "analytical" if possible, otherwise "deSolve" if a compiler is present, and "eigen" if no compiler is present and the model -can be expressed using eigenvalues and eigenvectors.</p></td> - </tr> - <tr> - <th>method.ode</th> - <td><p>The solution method passed via <code><a href='mkinpredict.html'>mkinpredict()</a></code> -to <code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code> in case the solution type is "deSolve". The default -"lsoda" is performant, but sometimes fails to converge.</p></td> - </tr> - <tr> - <th>use_compiled</th> - <td><p>If set to <code>FALSE</code>, no compiled version of the -<a href='mkinmod.html'>mkinmod</a> model is used in the calls to <code><a href='mkinpredict.html'>mkinpredict()</a></code> even if a compiled -version is present.</p></td> - </tr> - <tr> - <th>control</th> - <td><p>A list of control arguments passed to <code><a href='https://rdrr.io/r/stats/nlminb.html'>stats::nlminb()</a></code>.</p></td> - </tr> - <tr> - <th>transform_rates</th> - <td><p>Boolean specifying if kinetic rate constants should +can be expressed using eigenvalues and eigenvectors.</p></dd> + + +<dt>method.ode</dt> +<dd><p>The solution method passed via <code><a href="mkinpredict.html">mkinpredict()</a></code> +to <code><a href="https://rdrr.io/pkg/deSolve/man/ode.html" class="external-link">deSolve::ode()</a></code> in case the solution type is "deSolve". The default +"lsoda" is performant, but sometimes fails to converge.</p></dd> + + +<dt>use_compiled</dt> +<dd><p>If set to <code>FALSE</code>, no compiled version of the +<a href="mkinmod.html">mkinmod</a> model is used in the calls to <code><a href="mkinpredict.html">mkinpredict()</a></code> even if a compiled +version is present.</p></dd> + + +<dt>control</dt> +<dd><p>A list of control arguments passed to <code><a href="https://rdrr.io/r/stats/nlminb.html" class="external-link">stats::nlminb()</a></code>.</p></dd> + + +<dt>transform_rates</dt> +<dd><p>Boolean specifying if kinetic rate constants should be transformed in the model specification used in the fitting for better compliance with the assumption of normal distribution of the estimator. If TRUE, also alpha and beta parameters of the FOMC model are log-transformed, as well as k1 and k2 rate constants for the DFOP and HS models and the break point tb of the HS model. If FALSE, zero is used as -a lower bound for the rates in the optimisation.</p></td> - </tr> - <tr> - <th>transform_fractions</th> - <td><p>Boolean specifying if formation fractions +a lower bound for the rates in the optimisation.</p></dd> + + +<dt>transform_fractions</dt> +<dd><p>Boolean specifying if formation fractions should be transformed in the model specification used in the fitting for better compliance with the assumption of normal distribution of the estimator. The default (TRUE) is to do transformations. If TRUE, the g parameter of the DFOP model is also transformed. Transformations -are described in <a href='transform_odeparms.html'>transform_odeparms</a>.</p></td> - </tr> - <tr> - <th>quiet</th> - <td><p>Suppress printing out the current value of the negative -log-likelihood after each improvement?</p></td> - </tr> - <tr> - <th>atol</th> - <td><p>Absolute error tolerance, passed to <code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code>. Default -is 1e-8, which is lower than the default in the <code><a href='https://rdrr.io/pkg/deSolve/man/lsoda.html'>deSolve::lsoda()</a></code> -function which is used per default.</p></td> - </tr> - <tr> - <th>rtol</th> - <td><p>Absolute error tolerance, passed to <code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code>. Default -is 1e-10, much lower than in <code><a href='https://rdrr.io/pkg/deSolve/man/lsoda.html'>deSolve::lsoda()</a></code>.</p></td> - </tr> - <tr> - <th>error_model</th> - <td><p>If the error model is "const", a constant standard +are described in <a href="transform_odeparms.html">transform_odeparms</a>.</p></dd> + + +<dt>quiet</dt> +<dd><p>Suppress printing out the current value of the negative +log-likelihood after each improvement?</p></dd> + + +<dt>atol</dt> +<dd><p>Absolute error tolerance, passed to <code><a href="https://rdrr.io/pkg/deSolve/man/ode.html" class="external-link">deSolve::ode()</a></code>. Default +is 1e-8, which is lower than the default in the <code><a href="https://rdrr.io/pkg/deSolve/man/lsoda.html" class="external-link">deSolve::lsoda()</a></code> +function which is used per default.</p></dd> + + +<dt>rtol</dt> +<dd><p>Absolute error tolerance, passed to <code><a href="https://rdrr.io/pkg/deSolve/man/ode.html" class="external-link">deSolve::ode()</a></code>. Default +is 1e-10, much lower than in <code><a href="https://rdrr.io/pkg/deSolve/man/lsoda.html" class="external-link">deSolve::lsoda()</a></code>.</p></dd> + + +<dt>error_model</dt> +<dd><p>If the error model is "const", a constant standard deviation is assumed.</p> <p>If the error model is "obs", each observed variable is assumed to have its own variance.</p> @@ -340,11 +279,11 @@ error model similar to the one described by Rocke and Lorenzato (1995) is used for setting up the likelihood function. Note that this model deviates from the model by Rocke and Lorenzato, as their model implies that the errors follow a lognormal distribution for large values, not a -normal distribution as assumed by this method.</p></td> - </tr> - <tr> - <th>error_model_algorithm</th> - <td><p>If "auto", the selected algorithm depends on +normal distribution as assumed by this method.</p></dd> + + +<dt>error_model_algorithm</dt> +<dd><p>If "auto", the selected algorithm depends on the error model. If the error model is "const", unweighted nonlinear least squares fitting ("OLS") is selected. If the error model is "obs", or "tc", the "d_3" algorithm is selected.</p> @@ -367,372 +306,391 @@ degradation and error model parameters.</p> unweighted least squares, and then iterates optimization of the error model parameters and subsequent optimization of the degradation model using those error model parameters, until the error model parameters -converge.</p></td> - </tr> - <tr> - <th>reweight.tol</th> - <td><p>Tolerance for the convergence criterion calculated from -the error model parameters in IRLS fits.</p></td> - </tr> - <tr> - <th>reweight.max.iter</th> - <td><p>Maximum number of iterations in IRLS fits.</p></td> - </tr> - <tr> - <th>trace_parms</th> - <td><p>Should a trace of the parameter values be listed?</p></td> - </tr> - <tr> - <th>test_residuals</th> - <td><p>Should the residuals be tested for normal distribution?</p></td> - </tr> - <tr> - <th>...</th> - <td><p>Further arguments that will be passed on to -<code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code>.</p></td> - </tr> - </table> - - <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2> - - <p>A list with "mkinfit" in the class attribute.</p> - <h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2> +converge.</p></dd> + + +<dt>reweight.tol</dt> +<dd><p>Tolerance for the convergence criterion calculated from +the error model parameters in IRLS fits.</p></dd> + +<dt>reweight.max.iter</dt> +<dd><p>Maximum number of iterations in IRLS fits.</p></dd> + + +<dt>trace_parms</dt> +<dd><p>Should a trace of the parameter values be listed?</p></dd> + + +<dt>test_residuals</dt> +<dd><p>Should the residuals be tested for normal distribution?</p></dd> + + +<dt>...</dt> +<dd><p>Further arguments that will be passed on to +<code><a href="https://rdrr.io/pkg/deSolve/man/ode.html" class="external-link">deSolve::ode()</a></code>.</p></dd> + +</dl></div> + <div id="value"> + <h2>Value</h2> + + +<p>A list with "mkinfit" in the class attribute.</p> + </div> + <div id="details"> + <h2>Details</h2> <p>Per default, parameters in the kinetic models are internally transformed in order to better satisfy the assumption of a normal distribution of their estimators.</p> - <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2> - + </div> + <div id="note"> + <h2>Note</h2> <p>When using the "IORE" submodel for metabolites, fitting with "transform_rates = TRUE" (the default) often leads to failures of the numerical ODE solver. In this situation it may help to switch off the internal rate transformation.</p> - <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2> - + </div> + <div id="references"> + <h2>References</h2> <p>Rocke DM and Lorenzato S (1995) A two-component model for measurement error in analytical chemistry. <em>Technometrics</em> 37(2), 176-184.</p> <p>Ranke J and Meinecke S (2019) Error Models for the Kinetic Evaluation of Chemical Degradation Data. <em>Environments</em> 6(12) 124 -doi: <a href='https://doi.org/10.3390/environments6120124'>10.3390/environments6120124</a> +<a href="https://doi.org/10.3390/environments6120124" class="external-link">doi:10.3390/environments6120124</a> .</p> - <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2> - - <div class='dont-index'><p><a href='summary.mkinfit.html'>summary.mkinfit</a>, <a href='plot.mkinfit.html'>plot.mkinfit</a>, <a href='parms.html'>parms</a> and <a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a>.</p> + </div> + <div id="see-also"> + <h2>See also</h2> + <div class="dont-index"><p><a href="summary.mkinfit.html">summary.mkinfit</a>, <a href="plot.mkinfit.html">plot.mkinfit</a>, <a href="parms.html">parms</a> and <a href="https://rdrr.io/pkg/lmtest/man/lrtest.html" class="external-link">lrtest</a>.</p> <p>Comparisons of models fitted to the same data can be made using -<code><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></code> by virtue of the method <code><a href='logLik.mkinfit.html'>logLik.mkinfit</a></code>.</p> +<code><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></code> by virtue of the method <code><a href="logLik.mkinfit.html">logLik.mkinfit</a></code>.</p> <p>Fitting of several models to several datasets in a single call to -<code><a href='mmkin.html'>mmkin</a></code>.</p></div> - <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2> - +<code><a href="mmkin.html">mmkin</a></code>.</p></div> + </div> + <div id="author"> + <h2>Author</h2> <p>Johannes Ranke</p> + </div> - <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2> - <pre class="examples"><div class='input'> -<span class='co'># Use shorthand notation for parent only degradation</span> -<span class='va'>fit</span> <span class='op'><-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='st'>"FOMC"</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/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span> -</div><div class='output co'>#> mkin version used for fitting: 1.0.3.9000 -#> R version used for fitting: 4.0.3 -#> Date of fit: Mon Feb 15 17:09:39 2021 -#> Date of summary: Mon Feb 15 17:09:39 2021 -#> -#> Equations: -#> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent -#> -#> Model predictions using solution type analytical -#> -#> Fitted using 222 model solutions performed in 0.045 s -#> -#> Error model: Constant variance -#> -#> Error model algorithm: OLS -#> -#> Starting values for parameters to be optimised: -#> value type -#> parent_0 85.1 state -#> alpha 1.0 deparm -#> beta 10.0 deparm -#> -#> Starting values for the transformed parameters actually optimised: -#> value lower upper -#> parent_0 85.100000 -Inf Inf -#> log_alpha 0.000000 -Inf Inf -#> log_beta 2.302585 -Inf Inf -#> -#> Fixed parameter values: -#> None -#> -#> Results: -#> -#> AIC BIC logLik -#> 44.68652 45.47542 -18.34326 -#> -#> Optimised, transformed parameters with symmetric confidence intervals: -#> Estimate Std. Error Lower Upper -#> parent_0 85.87000 1.8070 81.23000 90.5200 -#> log_alpha 0.05192 0.1353 -0.29580 0.3996 -#> log_beta 0.65100 0.2287 0.06315 1.2390 -#> sigma 1.85700 0.4378 0.73200 2.9830 -#> -#> Parameter correlation: -#> parent_0 log_alpha log_beta sigma -#> parent_0 1.000e+00 -1.565e-01 -3.142e-01 4.772e-08 -#> log_alpha -1.565e-01 1.000e+00 9.564e-01 1.005e-07 -#> log_beta -3.142e-01 9.564e-01 1.000e+00 8.541e-08 -#> sigma 4.772e-08 1.005e-07 8.541e-08 1.000e+00 -#> -#> Backtransformed parameters: -#> Confidence intervals for internally transformed parameters are asymmetric. -#> t-test (unrealistically) based on the assumption of normal distribution -#> for estimators of untransformed parameters. -#> Estimate t value Pr(>t) Lower Upper -#> parent_0 85.870 47.530 3.893e-08 81.2300 90.520 -#> alpha 1.053 7.393 3.562e-04 0.7439 1.491 -#> beta 1.917 4.373 3.601e-03 1.0650 3.451 -#> sigma 1.857 4.243 4.074e-03 0.7320 2.983 -#> -#> FOCUS Chi2 error levels in percent: -#> err.min n.optim df -#> All data 6.657 3 6 -#> parent 6.657 3 6 -#> -#> Estimated disappearance times: -#> DT50 DT90 DT50back -#> parent 1.785 15.15 4.56 -#> -#> Data: -#> time variable observed predicted residual -#> 0 parent 85.1 85.875 -0.7749 -#> 1 parent 57.9 55.191 2.7091 -#> 3 parent 29.9 31.845 -1.9452 -#> 7 parent 14.6 17.012 -2.4124 -#> 14 parent 9.7 9.241 0.4590 -#> 28 parent 6.6 4.754 1.8460 -#> 63 parent 4.0 2.102 1.8977 -#> 91 parent 3.9 1.441 2.4590 -#> 119 parent 0.6 1.092 -0.4919</div><div class='input'> -<span class='co'># One parent compound, one metabolite, both single first order.</span> -<span class='co'># We remove zero values from FOCUS dataset D in order to avoid warnings</span> -<span class='va'>FOCUS_D</span> <span class='op'><-</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> -<span class='co'># Use mkinsub for convenience in model formulation. Pathway to sink included per default.</span> -<span class='va'>SFO_SFO</span> <span class='op'><-</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 class='op'>)</span> -</div><div class='output co'>#> <span class='message'>Temporary DLL for differentials generated and loaded</span></div><div class='input'> -<span class='co'># Fit the model quietly to the FOCUS example dataset D using defaults</span> -<span class='va'>fit</span> <span class='op'><-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span> -<span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span> -</div><div class='img'><img src='mkinfit-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># As lower parent values appear to have lower variance, we try an alternative error model</span> -<span class='va'>fit.tc</span> <span class='op'><-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span> -<span class='co'># This avoids the warning, and the likelihood ratio test confirms it is preferable</span> -<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span><span class='op'>(</span><span class='va'>fit.tc</span>, <span class='va'>fit</span><span class='op'>)</span> -</div><div class='output co'>#> Likelihood ratio test -#> -#> Model 1: SFO_SFO with error model tc and fixed parameter(s) m1_0 -#> Model 2: SFO_SFO with error model const and fixed parameter(s) m1_0 -#> #Df LogLik Df Chisq Pr(>Chisq) -#> 1 6 -64.983 -#> 2 5 -97.224 -1 64.483 9.737e-16 *** -#> --- -#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='co'># We can also allow for different variances of parent and metabolite as error model</span> -<span class='va'>fit.obs</span> <span class='op'><-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"obs"</span><span class='op'>)</span> -<span class='co'># The two-component error model has significantly higher likelihood</span> -<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span><span class='op'>(</span><span class='va'>fit.obs</span>, <span class='va'>fit.tc</span><span class='op'>)</span> -</div><div class='output co'>#> Likelihood ratio test -#> -#> Model 1: SFO_SFO with error model tc and fixed parameter(s) m1_0 -#> Model 2: SFO_SFO with error model obs and fixed parameter(s) m1_0 -#> #Df LogLik Df Chisq Pr(>Chisq) -#> 1 6 -64.983 -#> 2 6 -96.936 0 63.907 < 2.2e-16 *** -#> --- -#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='fu'><a href='parms.html'>parms</a></span><span class='op'>(</span><span class='va'>fit.tc</span><span class='op'>)</span> -</div><div class='output co'>#> parent_0 k_parent k_m1 f_parent_to_m1 sigma_low -#> 1.007343e+02 1.005562e-01 5.166712e-03 5.083933e-01 3.049883e-03 -#> rsd_high -#> 7.928118e-02 </div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>fit.tc</span><span class='op'>)</span> -</div><div class='output co'>#> $ff -#> parent_m1 parent_sink -#> 0.5083933 0.4916067 -#> -#> $distimes -#> DT50 DT90 -#> parent 6.89313 22.89848 -#> m1 134.15634 445.65772 -#> </div><div class='input'> -<span class='co'># We can show a quick (only one replication) benchmark for this case, as we</span> -<span class='co'># have several alternative solution methods for the model. We skip</span> -<span class='co'># uncompiled deSolve, as it is so slow. More benchmarks are found in the</span> -<span class='co'># benchmark vignette</span> -<span class='co'># \dontrun{</span> -<span class='kw'>if</span><span class='op'>(</span><span class='kw'><a href='https://rdrr.io/r/base/library.html'>require</a></span><span class='op'>(</span><span class='va'><a href='http://rbenchmark.googlecode.com'>rbenchmark</a></span><span class='op'>)</span><span class='op'>)</span> <span class='op'>{</span> - <span class='fu'><a href='https://rdrr.io/pkg/rbenchmark/man/benchmark.html'>benchmark</a></span><span class='op'>(</span>replications <span class='op'>=</span> <span class='fl'>1</span>, order <span class='op'>=</span> <span class='st'>"relative"</span>, columns <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'>"test"</span>, <span class='st'>"relative"</span>, <span class='st'>"elapsed"</span><span class='op'>)</span>, - deSolve_compiled <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>, - solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>, use_compiled <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>, - eigen <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>, - solution_type <span class='op'>=</span> <span class='st'>"eigen"</span><span class='op'>)</span>, - analytical <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>, - solution_type <span class='op'>=</span> <span class='st'>"analytical"</span><span class='op'>)</span><span class='op'>)</span> -<span class='op'>}</span> -</div><div class='output co'>#> test relative elapsed -#> 3 analytical 1.000 0.563 -#> 1 deSolve_compiled 1.702 0.958 -#> 2 eigen 2.597 1.462</div><div class='input'><span class='co'># }</span> - -<span class='co'># Use stepwise fitting, using optimised parameters from parent only fit, FOMC-SFO</span> -<span class='co'># \dontrun{</span> -<span class='va'>FOMC_SFO</span> <span class='op'><-</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'>"FOMC"</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 class='op'>)</span> -</div><div class='output co'>#> <span class='message'>Temporary DLL for differentials generated and loaded</span></div><div class='input'><span class='va'>fit.FOMC_SFO</span> <span class='op'><-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>FOMC_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span> -<span class='co'># Again, we get a warning and try a more sophisticated error model</span> -<span class='va'>fit.FOMC_SFO.tc</span> <span class='op'><-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>FOMC_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span> -<span class='co'># This model has a higher likelihood, but not significantly so</span> -<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span><span class='op'>(</span><span class='va'>fit.tc</span>, <span class='va'>fit.FOMC_SFO.tc</span><span class='op'>)</span> -</div><div class='output co'>#> Likelihood ratio test -#> -#> Model 1: FOMC_SFO with error model tc and fixed parameter(s) m1_0 -#> Model 2: SFO_SFO with error model tc and fixed parameter(s) m1_0 -#> #Df LogLik Df Chisq Pr(>Chisq) -#> 1 7 -64.829 -#> 2 6 -64.983 -1 0.3075 0.5792</div><div class='input'><span class='co'># Also, the missing standard error for log_beta and the t-tests for alpha</span> -<span class='co'># and beta indicate overparameterisation</span> -<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>fit.FOMC_SFO.tc</span>, data <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span> -</div><div class='output co'>#> <span class='warning'>Warning: NaNs produced</span></div><div class='output co'>#> <span class='warning'>Warning: NaNs produced</span></div><div class='output co'>#> <span class='warning'>Warning: diag(.) had 0 or NA entries; non-finite result is doubtful</span></div><div class='output co'>#> mkin version used for fitting: 1.0.3.9000 -#> R version used for fitting: 4.0.3 -#> Date of fit: Mon Feb 15 17:09:50 2021 -#> Date of summary: Mon Feb 15 17:09:50 2021 -#> -#> Equations: -#> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent -#> d_m1/dt = + f_parent_to_m1 * (alpha/beta) * 1/((time/beta) + 1) * -#> parent - k_m1 * m1 -#> -#> Model predictions using solution type deSolve -#> -#> Fitted using 3729 model solutions performed in 2.815 s -#> -#> Error model: Two-component variance function -#> -#> Error model algorithm: d_3 -#> Direct fitting and three-step fitting yield approximately the same likelihood -#> -#> Starting values for parameters to be optimised: -#> value type -#> parent_0 100.75 state -#> alpha 1.00 deparm -#> beta 10.00 deparm -#> k_m1 0.10 deparm -#> f_parent_to_m1 0.50 deparm -#> sigma_low 0.10 error -#> rsd_high 0.10 error -#> -#> Starting values for the transformed parameters actually optimised: -#> value lower upper -#> parent_0 100.750000 -Inf Inf -#> log_k_m1 -2.302585 -Inf Inf -#> f_parent_qlogis 0.000000 -Inf Inf -#> log_alpha 0.000000 -Inf Inf -#> log_beta 2.302585 -Inf Inf -#> sigma_low 0.100000 0 Inf -#> rsd_high 0.100000 0 Inf -#> -#> Fixed parameter values: -#> value type -#> m1_0 0 state -#> -#> Results: -#> -#> AIC BIC logLik -#> 143.658 155.1211 -64.82902 -#> -#> Optimised, transformed parameters with symmetric confidence intervals: -#> Estimate Std. Error Lower Upper -#> parent_0 101.600000 2.6400000 96.240000 107.000000 -#> log_k_m1 -5.284000 0.0929100 -5.474000 -5.095000 -#> f_parent_qlogis 0.001426 0.0767000 -0.155000 0.157800 -#> log_alpha 5.522000 0.0077320 5.506000 5.538000 -#> log_beta 7.806000 NaN NaN NaN -#> sigma_low 0.002488 0.0002431 0.001992 0.002984 -#> rsd_high 0.079210 0.0093280 0.060180 0.098230 -#> -#> Parameter correlation: -#> parent_0 log_k_m1 f_parent_qlogis log_alpha log_beta -#> parent_0 1.000000 -0.095226 -0.76678 0.70544 NaN -#> log_k_m1 -0.095226 1.000000 0.51432 -0.14387 NaN -#> f_parent_qlogis -0.766780 0.514321 1.00000 -0.61396 NaN -#> log_alpha 0.705444 -0.143872 -0.61396 1.00000 NaN -#> log_beta NaN NaN NaN NaN 1 -#> sigma_low 0.016073 0.001586 0.01548 5.87007 NaN -#> rsd_high 0.006626 -0.011700 -0.05357 0.04849 NaN -#> sigma_low rsd_high -#> parent_0 0.016073 0.006626 -#> log_k_m1 0.001586 -0.011700 -#> f_parent_qlogis 0.015476 -0.053566 -#> log_alpha 5.870075 0.048487 -#> log_beta NaN NaN -#> sigma_low 1.000000 -0.652558 -#> rsd_high -0.652558 1.000000 -#> -#> Backtransformed parameters: -#> Confidence intervals for internally transformed parameters are asymmetric. -#> t-test (unrealistically) based on the assumption of normal distribution -#> for estimators of untransformed parameters. -#> Estimate t value Pr(>t) Lower Upper -#> parent_0 1.016e+02 32.7800 6.311e-26 9.624e+01 1.070e+02 -#> k_m1 5.072e-03 10.1200 1.216e-11 4.196e-03 6.130e-03 -#> f_parent_to_m1 5.004e-01 20.8300 4.317e-20 4.613e-01 5.394e-01 -#> alpha 2.502e+02 0.5624 2.889e-01 2.463e+02 2.542e+02 -#> beta 2.455e+03 0.5549 2.915e-01 NA NA -#> sigma_low 2.488e-03 0.4843 3.158e-01 1.992e-03 2.984e-03 -#> rsd_high 7.921e-02 8.4300 8.001e-10 6.018e-02 9.823e-02 -#> -#> FOCUS Chi2 error levels in percent: -#> err.min n.optim df -#> All data 6.781 5 14 -#> parent 7.141 3 6 -#> m1 4.640 2 8 -#> -#> Resulting formation fractions: -#> ff -#> parent_m1 0.5004 -#> parent_sink 0.4996 -#> -#> Estimated disappearance times: -#> DT50 DT90 DT50back -#> parent 6.812 22.7 6.834 -#> m1 136.661 454.0 NA</div><div class='input'> -<span class='co'># We can easily use starting parameters from the parent only fit (only for illustration)</span> -<span class='va'>fit.FOMC</span> <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='va'>FOCUS_2006_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span> -<span class='va'>fit.FOMC_SFO</span> <span class='op'><-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>FOMC_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, - parms.ini <span class='op'>=</span> <span class='va'>fit.FOMC</span><span class='op'>$</span><span class='va'>bparms.ode</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span> -<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></span> +<span class="r-in"><span><span class="co"># Use shorthand notation for parent only degradation</span></span></span> +<span class="r-in"><span><span class="va">fit</span> <span class="op"><-</span> <span class="fu">mkinfit</span><span class="op">(</span><span class="st">"FOMC"</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/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fit</span><span class="op">)</span></span></span> +<span class="r-out co"><span class="r-pr">#></span> mkin version used for fitting: 1.1.2 </span> +<span class="r-out co"><span class="r-pr">#></span> R version used for fitting: 4.2.1 </span> +<span class="r-out co"><span class="r-pr">#></span> Date of fit: Wed Aug 10 15:24:16 2022 </span> +<span class="r-out co"><span class="r-pr">#></span> Date of summary: Wed Aug 10 15:24:16 2022 </span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Equations:</span> +<span class="r-out co"><span class="r-pr">#></span> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Model predictions using solution type analytical </span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Fitted using 222 model solutions performed in 0.045 s</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Error model: Constant variance </span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Error model algorithm: OLS </span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Starting values for parameters to be optimised:</span> +<span class="r-out co"><span class="r-pr">#></span> value type</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 85.1 state</span> +<span class="r-out co"><span class="r-pr">#></span> alpha 1.0 deparm</span> +<span class="r-out co"><span class="r-pr">#></span> beta 10.0 deparm</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Starting values for the transformed parameters actually optimised:</span> +<span class="r-out co"><span class="r-pr">#></span> value lower upper</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 85.100000 -Inf Inf</span> +<span class="r-out co"><span class="r-pr">#></span> log_alpha 0.000000 -Inf Inf</span> +<span class="r-out co"><span class="r-pr">#></span> log_beta 2.302585 -Inf Inf</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Fixed parameter values:</span> +<span class="r-out co"><span class="r-pr">#></span> None</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Results:</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> AIC BIC logLik</span> +<span class="r-out co"><span class="r-pr">#></span> 44.68652 45.47542 -18.34326</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Optimised, transformed parameters with symmetric confidence intervals:</span> +<span class="r-out co"><span class="r-pr">#></span> Estimate Std. Error Lower Upper</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 85.87000 1.8070 81.23000 90.5200</span> +<span class="r-out co"><span class="r-pr">#></span> log_alpha 0.05192 0.1353 -0.29580 0.3996</span> +<span class="r-out co"><span class="r-pr">#></span> log_beta 0.65100 0.2287 0.06315 1.2390</span> +<span class="r-out co"><span class="r-pr">#></span> sigma 1.85700 0.4378 0.73200 2.9830</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Parameter correlation:</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 log_alpha log_beta sigma</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 1.000e+00 -1.565e-01 -3.142e-01 4.772e-08</span> +<span class="r-out co"><span class="r-pr">#></span> log_alpha -1.565e-01 1.000e+00 9.564e-01 1.005e-07</span> +<span class="r-out co"><span class="r-pr">#></span> log_beta -3.142e-01 9.564e-01 1.000e+00 8.541e-08</span> +<span class="r-out co"><span class="r-pr">#></span> sigma 4.772e-08 1.005e-07 8.541e-08 1.000e+00</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Backtransformed parameters:</span> +<span class="r-out co"><span class="r-pr">#></span> Confidence intervals for internally transformed parameters are asymmetric.</span> +<span class="r-out co"><span class="r-pr">#></span> t-test (unrealistically) based on the assumption of normal distribution</span> +<span class="r-out co"><span class="r-pr">#></span> for estimators of untransformed parameters.</span> +<span class="r-out co"><span class="r-pr">#></span> Estimate t value Pr(>t) Lower Upper</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 85.870 47.530 3.893e-08 81.2300 90.520</span> +<span class="r-out co"><span class="r-pr">#></span> alpha 1.053 7.393 3.562e-04 0.7439 1.491</span> +<span class="r-out co"><span class="r-pr">#></span> beta 1.917 4.373 3.601e-03 1.0650 3.451</span> +<span class="r-out co"><span class="r-pr">#></span> sigma 1.857 4.243 4.074e-03 0.7320 2.983</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> FOCUS Chi2 error levels in percent:</span> +<span class="r-out co"><span class="r-pr">#></span> err.min n.optim df</span> +<span class="r-out co"><span class="r-pr">#></span> All data 6.657 3 6</span> +<span class="r-out co"><span class="r-pr">#></span> parent 6.657 3 6</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Estimated disappearance times:</span> +<span class="r-out co"><span class="r-pr">#></span> DT50 DT90 DT50back</span> +<span class="r-out co"><span class="r-pr">#></span> parent 1.785 15.15 4.56</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Data:</span> +<span class="r-out co"><span class="r-pr">#></span> time variable observed predicted residual</span> +<span class="r-out co"><span class="r-pr">#></span> 0 parent 85.1 85.875 -0.7749</span> +<span class="r-out co"><span class="r-pr">#></span> 1 parent 57.9 55.191 2.7091</span> +<span class="r-out co"><span class="r-pr">#></span> 3 parent 29.9 31.845 -1.9452</span> +<span class="r-out co"><span class="r-pr">#></span> 7 parent 14.6 17.012 -2.4124</span> +<span class="r-out co"><span class="r-pr">#></span> 14 parent 9.7 9.241 0.4590</span> +<span class="r-out co"><span class="r-pr">#></span> 28 parent 6.6 4.754 1.8460</span> +<span class="r-out co"><span class="r-pr">#></span> 63 parent 4.0 2.102 1.8977</span> +<span class="r-out co"><span class="r-pr">#></span> 91 parent 3.9 1.441 2.4590</span> +<span class="r-out co"><span class="r-pr">#></span> 119 parent 0.6 1.092 -0.4919</span> +<span class="r-in"><span></span></span> +<span class="r-in"><span><span class="co"># One parent compound, one metabolite, both single first order.</span></span></span> +<span class="r-in"><span><span class="co"># We remove zero values from FOCUS dataset D in order to avoid warnings</span></span></span> +<span class="r-in"><span><span class="va">FOCUS_D</span> <span class="op"><-</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></span></span> +<span class="r-in"><span><span class="co"># Use mkinsub for convenience in model formulation. Pathway to sink included per default.</span></span></span> +<span class="r-in"><span><span class="va">SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="mkinmod.html">mkinmod</a></span><span class="op">(</span></span></span> +<span class="r-in"><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>,</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 class="op">)</span></span></span> +<span class="r-msg co"><span class="r-pr">#></span> Temporary DLL for differentials generated and loaded</span> +<span class="r-in"><span></span></span> +<span class="r-in"><span><span class="co"># Fit the model quietly to the FOCUS example dataset D using defaults</span></span></span> +<span class="r-in"><span><span class="va">fit</span> <span class="op"><-</span> <span class="fu">mkinfit</span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</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="plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">fit</span><span class="op">)</span></span></span> +<span class="r-plt img"><img src="mkinfit-1.png" alt="" width="700" height="433"></span> +<span class="r-in"><span><span class="co"># As lower parent values appear to have lower variance, we try an alternative error model</span></span></span> +<span class="r-in"><span><span class="va">fit.tc</span> <span class="op"><-</span> <span class="fu">mkinfit</span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="co"># This avoids the warning, and the likelihood ratio test confirms it is preferable</span></span></span> +<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/pkg/lmtest/man/lrtest.html" class="external-link">lrtest</a></span><span class="op">(</span><span class="va">fit.tc</span>, <span class="va">fit</span><span class="op">)</span></span></span> +<span class="r-out co"><span class="r-pr">#></span> Likelihood ratio test</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Model 1: SFO_SFO with error model tc and fixed parameter(s) m1_0</span> +<span class="r-out co"><span class="r-pr">#></span> Model 2: SFO_SFO with error model const and fixed parameter(s) m1_0</span> +<span class="r-out co"><span class="r-pr">#></span> #Df LogLik Df Chisq Pr(>Chisq) </span> +<span class="r-out co"><span class="r-pr">#></span> 1 6 -64.983 </span> +<span class="r-out co"><span class="r-pr">#></span> 2 5 -97.224 -1 64.483 9.737e-16 ***</span> +<span class="r-out co"><span class="r-pr">#></span> ---</span> +<span class="r-out co"><span class="r-pr">#></span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span> +<span class="r-in"><span><span class="co"># We can also allow for different variances of parent and metabolite as error model</span></span></span> +<span class="r-in"><span><span class="va">fit.obs</span> <span class="op"><-</span> <span class="fu">mkinfit</span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, error_model <span class="op">=</span> <span class="st">"obs"</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="co"># The two-component error model has significantly higher likelihood</span></span></span> +<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/pkg/lmtest/man/lrtest.html" class="external-link">lrtest</a></span><span class="op">(</span><span class="va">fit.obs</span>, <span class="va">fit.tc</span><span class="op">)</span></span></span> +<span class="r-out co"><span class="r-pr">#></span> Likelihood ratio test</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Model 1: SFO_SFO with error model tc and fixed parameter(s) m1_0</span> +<span class="r-out co"><span class="r-pr">#></span> Model 2: SFO_SFO with error model obs and fixed parameter(s) m1_0</span> +<span class="r-out co"><span class="r-pr">#></span> #Df LogLik Df Chisq Pr(>Chisq) </span> +<span class="r-out co"><span class="r-pr">#></span> 1 6 -64.983 </span> +<span class="r-out co"><span class="r-pr">#></span> 2 6 -96.936 0 63.907 < 2.2e-16 ***</span> +<span class="r-out co"><span class="r-pr">#></span> ---</span> +<span class="r-out co"><span class="r-pr">#></span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span> +<span class="r-in"><span><span class="fu"><a href="parms.html">parms</a></span><span class="op">(</span><span class="va">fit.tc</span><span class="op">)</span></span></span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 k_parent k_m1 f_parent_to_m1 sigma_low </span> +<span class="r-out co"><span class="r-pr">#></span> 1.007343e+02 1.005562e-01 5.166712e-03 5.083933e-01 3.049883e-03 </span> +<span class="r-out co"><span class="r-pr">#></span> rsd_high </span> +<span class="r-out co"><span class="r-pr">#></span> 7.928118e-02 </span> +<span class="r-in"><span><span class="fu"><a href="endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fit.tc</span><span class="op">)</span></span></span> +<span class="r-out co"><span class="r-pr">#></span> $ff</span> +<span class="r-out co"><span class="r-pr">#></span> parent_m1 parent_sink </span> +<span class="r-out co"><span class="r-pr">#></span> 0.5083933 0.4916067 </span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> $distimes</span> +<span class="r-out co"><span class="r-pr">#></span> DT50 DT90</span> +<span class="r-out co"><span class="r-pr">#></span> parent 6.89313 22.89848</span> +<span class="r-out co"><span class="r-pr">#></span> m1 134.15634 445.65772</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-in"><span></span></span> +<span class="r-in"><span><span class="co"># We can show a quick (only one replication) benchmark for this case, as we</span></span></span> +<span class="r-in"><span><span class="co"># have several alternative solution methods for the model. We skip</span></span></span> +<span class="r-in"><span><span class="co"># uncompiled deSolve, as it is so slow. More benchmarks are found in the</span></span></span> +<span class="r-in"><span><span class="co"># benchmark vignette</span></span></span> +<span class="r-in"><span><span class="co"># \dontrun{</span></span></span> +<span class="r-in"><span><span class="kw">if</span><span class="op">(</span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">require</a></span><span class="op">(</span><span class="va"><a href="http://rbenchmark.googlecode.com" class="external-link">rbenchmark</a></span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span></span> +<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/pkg/rbenchmark/man/benchmark.html" class="external-link">benchmark</a></span><span class="op">(</span>replications <span class="op">=</span> <span class="fl">1</span>, order <span class="op">=</span> <span class="st">"relative"</span>, columns <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">"test"</span>, <span class="st">"relative"</span>, <span class="st">"elapsed"</span><span class="op">)</span>,</span></span> +<span class="r-in"><span> deSolve_compiled <span class="op">=</span> <span class="fu">mkinfit</span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>,</span></span> +<span class="r-in"><span> solution_type <span class="op">=</span> <span class="st">"deSolve"</span>, use_compiled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span></span> +<span class="r-in"><span> eigen <span class="op">=</span> <span class="fu">mkinfit</span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>,</span></span> +<span class="r-in"><span> solution_type <span class="op">=</span> <span class="st">"eigen"</span><span class="op">)</span>,</span></span> +<span class="r-in"><span> analytical <span class="op">=</span> <span class="fu">mkinfit</span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>,</span></span> +<span class="r-in"><span> solution_type <span class="op">=</span> <span class="st">"analytical"</span><span class="op">)</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="op">}</span></span></span> +<span class="r-out co"><span class="r-pr">#></span> test relative elapsed</span> +<span class="r-out co"><span class="r-pr">#></span> 3 analytical 1.000 0.605</span> +<span class="r-out co"><span class="r-pr">#></span> 1 deSolve_compiled 1.448 0.876</span> +<span class="r-out co"><span class="r-pr">#></span> 2 eigen 2.479 1.500</span> +<span class="r-in"><span><span class="co"># }</span></span></span> +<span class="r-in"><span></span></span> +<span class="r-in"><span><span class="co"># Use stepwise fitting, using optimised parameters from parent only fit, FOMC-SFO</span></span></span> +<span class="r-in"><span><span class="co"># \dontrun{</span></span></span> +<span class="r-in"><span><span class="va">FOMC_SFO</span> <span class="op"><-</span> <span class="fu"><a href="mkinmod.html">mkinmod</a></span><span class="op">(</span></span></span> +<span class="r-in"><span> parent <span class="op">=</span> <span class="fu"><a href="mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="st">"m1"</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 class="op">)</span></span></span> +<span class="r-msg co"><span class="r-pr">#></span> Temporary DLL for differentials generated and loaded</span> +<span class="r-in"><span><span class="va">fit.FOMC_SFO</span> <span class="op"><-</span> <span class="fu">mkinfit</span><span class="op">(</span><span class="va">FOMC_SFO</span>, <span class="va">FOCUS_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="co"># Again, we get a warning and try a more sophisticated error model</span></span></span> +<span class="r-in"><span><span class="va">fit.FOMC_SFO.tc</span> <span class="op"><-</span> <span class="fu">mkinfit</span><span class="op">(</span><span class="va">FOMC_SFO</span>, <span class="va">FOCUS_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="co"># This model has a higher likelihood, but not significantly so</span></span></span> +<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/pkg/lmtest/man/lrtest.html" class="external-link">lrtest</a></span><span class="op">(</span><span class="va">fit.tc</span>, <span class="va">fit.FOMC_SFO.tc</span><span class="op">)</span></span></span> +<span class="r-out co"><span class="r-pr">#></span> Likelihood ratio test</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Model 1: FOMC_SFO with error model tc and fixed parameter(s) m1_0</span> +<span class="r-out co"><span class="r-pr">#></span> Model 2: SFO_SFO with error model tc and fixed parameter(s) m1_0</span> +<span class="r-out co"><span class="r-pr">#></span> #Df LogLik Df Chisq Pr(>Chisq)</span> +<span class="r-out co"><span class="r-pr">#></span> 1 7 -64.829 </span> +<span class="r-out co"><span class="r-pr">#></span> 2 6 -64.983 -1 0.3075 0.5792</span> +<span class="r-in"><span><span class="co"># Also, the missing standard error for log_beta and the t-tests for alpha</span></span></span> +<span class="r-in"><span><span class="co"># and beta indicate overparameterisation</span></span></span> +<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fit.FOMC_SFO.tc</span>, data <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></span> +<span class="r-wrn co"><span class="r-pr">#></span> <span class="warning">Warning: </span>NaNs produced</span> +<span class="r-wrn co"><span class="r-pr">#></span> <span class="warning">Warning: </span>NaNs produced</span> +<span class="r-wrn co"><span class="r-pr">#></span> <span class="warning">Warning: </span>diag(.) had 0 or NA entries; non-finite result is doubtful</span> +<span class="r-out co"><span class="r-pr">#></span> mkin version used for fitting: 1.1.2 </span> +<span class="r-out co"><span class="r-pr">#></span> R version used for fitting: 4.2.1 </span> +<span class="r-out co"><span class="r-pr">#></span> Date of fit: Wed Aug 10 15:24:27 2022 </span> +<span class="r-out co"><span class="r-pr">#></span> Date of summary: Wed Aug 10 15:24:27 2022 </span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Equations:</span> +<span class="r-out co"><span class="r-pr">#></span> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent</span> +<span class="r-out co"><span class="r-pr">#></span> d_m1/dt = + f_parent_to_m1 * (alpha/beta) * 1/((time/beta) + 1) *</span> +<span class="r-out co"><span class="r-pr">#></span> parent - k_m1 * m1</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Model predictions using solution type deSolve </span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Fitted using 3729 model solutions performed in 2.475 s</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Error model: Two-component variance function </span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Error model algorithm: d_3 </span> +<span class="r-out co"><span class="r-pr">#></span> Direct fitting and three-step fitting yield approximately the same likelihood </span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Starting values for parameters to be optimised:</span> +<span class="r-out co"><span class="r-pr">#></span> value type</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 100.75 state</span> +<span class="r-out co"><span class="r-pr">#></span> alpha 1.00 deparm</span> +<span class="r-out co"><span class="r-pr">#></span> beta 10.00 deparm</span> +<span class="r-out co"><span class="r-pr">#></span> k_m1 0.10 deparm</span> +<span class="r-out co"><span class="r-pr">#></span> f_parent_to_m1 0.50 deparm</span> +<span class="r-out co"><span class="r-pr">#></span> sigma_low 0.10 error</span> +<span class="r-out co"><span class="r-pr">#></span> rsd_high 0.10 error</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Starting values for the transformed parameters actually optimised:</span> +<span class="r-out co"><span class="r-pr">#></span> value lower upper</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 100.750000 -Inf Inf</span> +<span class="r-out co"><span class="r-pr">#></span> log_k_m1 -2.302585 -Inf Inf</span> +<span class="r-out co"><span class="r-pr">#></span> f_parent_qlogis 0.000000 -Inf Inf</span> +<span class="r-out co"><span class="r-pr">#></span> log_alpha 0.000000 -Inf Inf</span> +<span class="r-out co"><span class="r-pr">#></span> log_beta 2.302585 -Inf Inf</span> +<span class="r-out co"><span class="r-pr">#></span> sigma_low 0.100000 0 Inf</span> +<span class="r-out co"><span class="r-pr">#></span> rsd_high 0.100000 0 Inf</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Fixed parameter values:</span> +<span class="r-out co"><span class="r-pr">#></span> value type</span> +<span class="r-out co"><span class="r-pr">#></span> m1_0 0 state</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Results:</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> AIC BIC logLik</span> +<span class="r-out co"><span class="r-pr">#></span> 143.658 155.1211 -64.82902</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Optimised, transformed parameters with symmetric confidence intervals:</span> +<span class="r-out co"><span class="r-pr">#></span> Estimate Std. Error Lower Upper</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 101.600000 2.6400000 96.240000 107.000000</span> +<span class="r-out co"><span class="r-pr">#></span> log_k_m1 -5.284000 0.0929100 -5.474000 -5.095000</span> +<span class="r-out co"><span class="r-pr">#></span> f_parent_qlogis 0.001426 0.0767000 -0.155000 0.157800</span> +<span class="r-out co"><span class="r-pr">#></span> log_alpha 5.522000 0.0077320 5.506000 5.538000</span> +<span class="r-out co"><span class="r-pr">#></span> log_beta 7.806000 NaN NaN NaN</span> +<span class="r-out co"><span class="r-pr">#></span> sigma_low 0.002488 0.0002431 0.001992 0.002984</span> +<span class="r-out co"><span class="r-pr">#></span> rsd_high 0.079210 0.0093280 0.060180 0.098230</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Parameter correlation:</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 log_k_m1 f_parent_qlogis log_alpha log_beta</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 1.000000 -0.095226 -0.76678 0.70544 NaN</span> +<span class="r-out co"><span class="r-pr">#></span> log_k_m1 -0.095226 1.000000 0.51432 -0.14387 NaN</span> +<span class="r-out co"><span class="r-pr">#></span> f_parent_qlogis -0.766780 0.514321 1.00000 -0.61396 NaN</span> +<span class="r-out co"><span class="r-pr">#></span> log_alpha 0.705444 -0.143872 -0.61396 1.00000 NaN</span> +<span class="r-out co"><span class="r-pr">#></span> log_beta NaN NaN NaN NaN 1</span> +<span class="r-out co"><span class="r-pr">#></span> sigma_low 0.016073 0.001586 0.01548 5.87007 NaN</span> +<span class="r-out co"><span class="r-pr">#></span> rsd_high 0.006626 -0.011700 -0.05357 0.04849 NaN</span> +<span class="r-out co"><span class="r-pr">#></span> sigma_low rsd_high</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 0.016073 0.006626</span> +<span class="r-out co"><span class="r-pr">#></span> log_k_m1 0.001586 -0.011700</span> +<span class="r-out co"><span class="r-pr">#></span> f_parent_qlogis 0.015476 -0.053566</span> +<span class="r-out co"><span class="r-pr">#></span> log_alpha 5.870075 0.048487</span> +<span class="r-out co"><span class="r-pr">#></span> log_beta NaN NaN</span> +<span class="r-out co"><span class="r-pr">#></span> sigma_low 1.000000 -0.652558</span> +<span class="r-out co"><span class="r-pr">#></span> rsd_high -0.652558 1.000000</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Backtransformed parameters:</span> +<span class="r-out co"><span class="r-pr">#></span> Confidence intervals for internally transformed parameters are asymmetric.</span> +<span class="r-out co"><span class="r-pr">#></span> t-test (unrealistically) based on the assumption of normal distribution</span> +<span class="r-out co"><span class="r-pr">#></span> for estimators of untransformed parameters.</span> +<span class="r-out co"><span class="r-pr">#></span> Estimate t value Pr(>t) Lower Upper</span> +<span class="r-out co"><span class="r-pr">#></span> parent_0 1.016e+02 32.7800 6.311e-26 9.624e+01 1.070e+02</span> +<span class="r-out co"><span class="r-pr">#></span> k_m1 5.072e-03 10.1200 1.216e-11 4.196e-03 6.130e-03</span> +<span class="r-out co"><span class="r-pr">#></span> f_parent_to_m1 5.004e-01 20.8300 4.317e-20 4.613e-01 5.394e-01</span> +<span class="r-out co"><span class="r-pr">#></span> alpha 2.502e+02 0.5624 2.889e-01 2.463e+02 2.542e+02</span> +<span class="r-out co"><span class="r-pr">#></span> beta 2.455e+03 0.5549 2.915e-01 NA NA</span> +<span class="r-out co"><span class="r-pr">#></span> sigma_low 2.488e-03 0.4843 3.158e-01 1.992e-03 2.984e-03</span> +<span class="r-out co"><span class="r-pr">#></span> rsd_high 7.921e-02 8.4300 8.001e-10 6.018e-02 9.823e-02</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> FOCUS Chi2 error levels in percent:</span> +<span class="r-out co"><span class="r-pr">#></span> err.min n.optim df</span> +<span class="r-out co"><span class="r-pr">#></span> All data 6.781 5 14</span> +<span class="r-out co"><span class="r-pr">#></span> parent 7.141 3 6</span> +<span class="r-out co"><span class="r-pr">#></span> m1 4.640 2 8</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Resulting formation fractions:</span> +<span class="r-out co"><span class="r-pr">#></span> ff</span> +<span class="r-out co"><span class="r-pr">#></span> parent_m1 0.5004</span> +<span class="r-out co"><span class="r-pr">#></span> parent_sink 0.4996</span> +<span class="r-out co"><span class="r-pr">#></span> </span> +<span class="r-out co"><span class="r-pr">#></span> Estimated disappearance times:</span> +<span class="r-out co"><span class="r-pr">#></span> DT50 DT90 DT50back</span> +<span class="r-out co"><span class="r-pr">#></span> parent 6.812 22.7 6.834</span> +<span class="r-out co"><span class="r-pr">#></span> m1 136.661 454.0 NA</span> +<span class="r-in"><span></span></span> +<span class="r-in"><span><span class="co"># We can easily use starting parameters from the parent only fit (only for illustration)</span></span></span> +<span class="r-in"><span><span class="va">fit.FOMC</span> <span class="op">=</span> <span class="fu">mkinfit</span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="va">FOCUS_2006_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="va">fit.FOMC_SFO</span> <span class="op"><-</span> <span class="fu">mkinfit</span><span class="op">(</span><span class="va">FOMC_SFO</span>, <span class="va">FOCUS_D</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>,</span></span> +<span class="r-in"><span> parms.ini <span class="op">=</span> <span class="va">fit.FOMC</span><span class="op">$</span><span class="va">bparms.ode</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="co"># }</span></span></span> +</code></pre></div> + </div> </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> + <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> + <footer><div class="copyright"> + <p></p><p>Developed by Johannes Ranke.</p> </div> <div class="pkgdown"> - <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p> + <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" 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