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In each step of the optimisation, the -kinetic model is solved using the function mkinpredict(), except -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]> -<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"> - 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<span class="fab fa-github fa-lg"></span> - - </a> -</li> - </ul></div><!--/.nav-collapse --> - </div><!--/.container --> -</div><!--/.navbar --> - - - - </header><div class="row"> - <div class="col-md-9 contents"> - <div class="page-header"> - <h1>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/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" 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 -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 -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> - - <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></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. -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></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 -not in the model gives an error.</p> -<p>It is possible to only specify a subset of the parameters that the model -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></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 -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></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></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></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></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></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" 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></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></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></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> -<p>If the error model is "tc" (two-component error model), a two component -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></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> -<p>The algorithm "d_3" will directly minimize the negative log-likelihood -and independently also use the three step algorithm described below. -The fit with the higher likelihood is returned.</p> -<p>The algorithm "direct" will directly minimize the negative log-likelihood.</p> -<p>The algorithm "twostep" will minimize the negative log-likelihood after an -initial unweighted least squares optimisation step.</p> -<p>The algorithm "threestep" starts with unweighted least squares, then -optimizes only the error model using the degradation model parameters -found, and then minimizes the negative log-likelihood with free -degradation and error model parameters.</p> -<p>The algorithm "fourstep" starts with unweighted least squares, then -optimizes only the error model using the degradation model parameters -found, then optimizes the degradation model again with fixed error model -parameters, and finally minimizes the negative log-likelihood with free -degradation and error model parameters.</p> -<p>The algorithm "IRLS" (Iteratively Reweighted Least Squares) starts with -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></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> - </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> - </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 -<a href="https://doi.org/10.3390/environments6120124" class="external-link">doi:10.3390/environments6120124</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" 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> - </div> - <div id="author"> - <h2>Author</h2> - <p>Johannes Ranke</p> - </div> - - <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: 1.2.3 </span> -<span class="r-out co"><span class="r-pr">#></span> R version used for fitting: 4.2.3 </span> -<span class="r-out co"><span class="r-pr">#></span> Date of fit: Sun Apr 16 08:30:40 2023 </span> -<span class="r-out co"><span class="r-pr">#></span> Date of summary: Sun Apr 16 08:30:40 2023 </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 0.014 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 0.236</span> -<span class="r-out co"><span class="r-pr">#></span> 1 deSolve_compiled 1.263 0.298</span> -<span class="r-out co"><span class="r-pr">#></span> 2 eigen 2.373 0.560</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: 1.2.3 </span> -<span class="r-out co"><span class="r-pr">#></span> R version used for fitting: 4.2.3 </span> -<span class="r-out co"><span class="r-pr">#></span> Date of fit: Sun Apr 16 08:30:44 2023 </span> -<span class="r-out co"><span class="r-pr">#></span> Date of summary: Sun Apr 16 08:30:44 2023 </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 0.688 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> -</div> - - - <footer><div class="copyright"> - <p></p><p>Developed by Johannes Ranke.</p> -</div> - -<div class="pkgdown"> - <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p> -</div> - - </footer></div> - - - - - - - </body></html> - |