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+<title>mkinfit. mkin 0.9-41</title>
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+ Johannes Ranke
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+ <header>
+
+ </header>
+
+ <h1>
+ Fit a kinetic model to data with one or more state variables
+</h1>
+
+<div class="row">
+ <div class="span8">
+ <h2>Usage</h2>
+ <pre><div>mkinfit(mkinmod, observed, parms.ini&nbsp;=&nbsp;"auto", state.ini&nbsp;=&nbsp;"auto", fixed_parms&nbsp;=&nbsp;NULL, fixed_initials&nbsp;=&nbsp;names(mkinmod$diffs)[-1], solution_type&nbsp;=&nbsp;c("auto", "analytical", "eigen", "deSolve"), method.ode&nbsp;=&nbsp;"lsoda", use_compiled&nbsp;=&nbsp;"auto", method.modFit&nbsp;=&nbsp;c("Port", "Marq", "SANN", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B"), maxit.modFit&nbsp;=&nbsp;"auto", control.modFit&nbsp;=&nbsp;list(), transform_rates&nbsp;=&nbsp;TRUE, transform_fractions&nbsp;=&nbsp;TRUE, plot&nbsp;=&nbsp;FALSE, quiet&nbsp;=&nbsp;FALSE, err&nbsp;=&nbsp;NULL, weight&nbsp;=&nbsp;"none", scaleVar&nbsp;=&nbsp;FALSE, atol&nbsp;=&nbsp;1e-8, rtol&nbsp;=&nbsp;1e-10, n.outtimes&nbsp;=&nbsp;100, reweight.method&nbsp;=&nbsp;NULL, reweight.tol&nbsp;=&nbsp;1e-8, reweight.max.iter&nbsp;=&nbsp;10, trace_parms&nbsp;=&nbsp;FALSE, ...)</div></pre>
+
+ <h2>Arguments</h2>
+ <dl>
+ <dt>mkinmod</dt>
+ <dd>
+ A list of class <code><a href='mkinmod.html'>mkinmod</a></code>, containing the kinetic model to be
+ fitted to the data, or one of the shorthand names ("SFO", "FOMC", "DFOP",
+ "HS", "SFORB"). If a shorthand name is given, a parent only degradation
+ model is generated for the variable with the highest value in
+ <code>observed</code>.
+ </dd>
+ <dt>observed</dt>
+ <dd>
+ The observed data. It has to be in the long format as described in
+ <code><a href='http://www.inside-r.org/packages/cran/FME/docs/modFit'>modFit</a></code>, i.e. 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. Optionally, a further column
+ can contain weights for each data point. If it is not named "err", its name
+ must be passed as a further argument named <code>err</code> which is then passed
+ on to <code><a href='http://www.inside-r.org/packages/cran/FME/docs/modFit'>modFit</a></code>.
+ </dd>
+ <dt>parms.ini</dt>
+ <dd>
+ 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.
+
+ 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.
+ </dd>
+ <dt>state.ini</dt>
+ <dd>
+ 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 <code><a href='mkinmod.html'>mkinmod</a></code>). 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.
+ </dd>
+ <dt>fixed_parms</dt>
+ <dd>
+ The names of parameters that should not be optimised but rather kept at the
+ values specified in <code>parms.ini</code>.
+ </dd>
+ <dt>fixed_initials</dt>
+ <dd>
+ 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.
+ </dd>
+ <dt>solution_type</dt>
+ <dd>
+ 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 ode solver from package
+ <code><a href='http://www.inside-r.org/packages/cran/deSolve/docs/deSolve'>deSolve</a></code> is used. If set to "analytical", an analytical
+ solution of the model is used. This is only implemented for simple
+ degradation experiments with only one state variable, i.e. with no
+ metabolites. The default is "auto", which uses "analytical" if possible,
+ otherwise "eigen" if the model can be expressed using eigenvalues and
+ eigenvectors, and finally "deSolve" for the remaining models (time
+ dependence of degradation rates and metabolites). This argument is passed
+ on to the helper function <code><a href='mkinpredict.html'>mkinpredict</a></code>.
+ </dd>
+ <dt>method.ode</dt>
+ <dd>
+ The solution method passed via <code><a href='mkinpredict.html'>mkinpredict</a></code> to
+ <code><a href='http://www.inside-r.org/packages/cran/deSolve/docs/ode'>ode</a></code> in case the solution type is "deSolve". The default
+ "lsoda" is performant, but sometimes fails to converge.
+ </dd>
+ <dt>use_compiled</dt>
+ <dd>
+ If set to <code>FALSE</code>, no compiled version of the <code><a href='mkinmod.html'>mkinmod</a></code>
+ model is used, in the calls to <code><a href='mkinpredict.html'>mkinpredict</a></code> even if
+ a compiled verion is present.
+ </dd>
+ <dt>method.modFit</dt>
+ <dd>
+ The optimisation method passed to <code><a href='http://www.inside-r.org/packages/cran/FME/docs/modFit'>modFit</a></code>.
+
+ In order to optimally deal with problems where local minima occur, the
+ "Port" algorithm is now used per default as it is less prone to get trapped
+ in local minima and depends less on starting values for parameters than
+ the Levenberg Marquardt variant selected by "Marq". However, "Port" needs
+ more iterations.
+
+ The former default "Marq" is the Levenberg Marquardt algorithm
+ <code><a href='http://www.inside-r.org/packages/cran/minpack.lm/docs/nls.lm'>nls.lm</a></code> from the package <code>minpack.lm</code> and usually needs
+ the least number of iterations.
+
+ The "Pseudo" algorithm is not included because it needs finite parameter bounds
+ which are currently not supported.
+
+ The "Newton" algorithm is not included because its number of iterations
+ can not be controlled by <code>control.modFit</code> and it does not appear
+ to provide advantages over the other algorithms.
+ </dd>
+ <dt>maxit.modFit</dt>
+ <dd>
+ Maximum number of iterations in the optimisation. If not "auto", this will
+ be passed to the method called by <code><a href='http://www.inside-r.org/packages/cran/FME/docs/modFit'>modFit</a></code>, overriding
+ what may be specified in the next argument <code>control.modFit</code>.
+ </dd>
+ <dt>control.modFit</dt>
+ <dd>
+ Additional arguments passed to the optimisation method used by
+ <code><a href='http://www.inside-r.org/packages/cran/FME/docs/modFit'>modFit</a></code>.
+ </dd>
+ <dt>transform_rates</dt>
+ <dd>
+ 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.
+ </dd>
+ <dt>transform_fractions</dt>
+ <dd>
+ Boolean specifying if formation fractions constants 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 and HS
+ models are also transformed, as they can also be seen as compositional
+ data. The transformation used for these transformations is the
+ <code><a href='ilr.html'>ilr</a></code> transformation.
+ </dd>
+ <dt>plot</dt>
+ <dd>
+ Should the observed values and the numerical solutions be plotted at each
+ stage of the optimisation?
+ </dd>
+ <dt>quiet</dt>
+ <dd>
+ Suppress printing out the current model cost after each improvement?
+ </dd>
+ <dt>err </dt>
+ <dd>either <code>NULL</code>, or the name of the column with the
+ <em>error</em> estimates, used to weigh the residuals (see details of
+ <code><a href='http://www.inside-r.org/packages/cran/FME/docs/modCost'>modCost</a></code>); if <code>NULL</code>, then the residuals are not weighed.
+ </dd>
+ <dt>weight</dt>
+ <dd>
+ only if <code>err</code>=<code>NULL</code>: how to weight the residuals, one of "none",
+ "std", "mean", see details of <code><a href='http://www.inside-r.org/packages/cran/FME/docs/modCost'>modCost</a></code>.
+ </dd>
+ <dt>scaleVar</dt>
+ <dd>
+ Will be passed to <code><a href='http://www.inside-r.org/packages/cran/FME/docs/modCost'>modCost</a></code>. Default is not to scale Variables
+ according to the number of observations.
+ </dd>
+ <dt>atol</dt>
+ <dd>
+ Absolute error tolerance, passed to <code><a href='http://www.inside-r.org/packages/cran/deSolve/docs/ode'>ode</a></code>. Default is 1e-8,
+ lower than in <code><a href='http://www.inside-r.org/packages/cran/deSolve/docs/lsoda'>lsoda</a></code>.
+ </dd>
+ <dt>rtol</dt>
+ <dd>
+ Absolute error tolerance, passed to <code><a href='http://www.inside-r.org/packages/cran/deSolve/docs/ode'>ode</a></code>. Default is 1e-10,
+ much lower than in <code><a href='http://www.inside-r.org/packages/cran/deSolve/docs/lsoda'>lsoda</a></code>.
+ </dd>
+ <dt>n.outtimes</dt>
+ <dd>
+ The length of the dataseries that is produced by the model prediction
+ function <code><a href='mkinpredict.html'>mkinpredict</a></code>. This impacts the accuracy of
+ the numerical solver if that is used (see <code>solution_type</code> argument.
+ The default value is 100.
+ </dd>
+ <dt>reweight.method</dt>
+ <dd>
+ The method used for iteratively reweighting residuals, also known
+ as iteratively reweighted least squares (IRLS). Default is NULL,
+ the other method implemented is called "obs", meaning that each
+ observed variable is assumed to have its own variance, this is
+ estimated from the fit and used for weighting the residuals
+ in each iteration until convergence of this estimate up to
+ <code>reweight.tol</code> or up to the maximum number of iterations
+ specified by <code>reweight.max.iter</code>.
+ </dd>
+ <dt>reweight.tol</dt>
+ <dd>
+ Tolerance for convergence criterion for the variance components
+ in IRLS fits.
+ </dd>
+ <dt>reweight.max.iter</dt>
+ <dd>
+ Maximum iterations in IRLS fits.
+ </dd>
+ <dt>trace_parms</dt>
+ <dd>
+ Should a trace of the parameter values be listed?
+ </dd>
+ <dt>...</dt>
+ <dd>
+ Further arguments that will be passed to <code><a href='http://www.inside-r.org/packages/cran/FME/docs/modFit'>modFit</a></code>.
+ </dd>
+ </dl>
+
+ <div class="Description">
+ <h2>Description</h2>
+
+ <p>This function uses the Flexible Modelling Environment package
+ <code><a href='http://www.inside-r.org/packages/cran/FME/docs/FME'>FME</a></code> to create a function calculating the model cost, i.e. the
+ deviation between the kinetic model and the observed data. This model cost is
+ then minimised using the Port algorithm <code><a href='http://www.inside-r.org/r-doc/stats/nlminb'>nlminb</a></code>,
+ using the specified initial or fixed parameters and starting values.
+ Per default, parameters in the kinetic models are internally transformed in order
+ to better satisfy the assumption of a normal distribution of their estimators.
+ In each step of the optimsation, the kinetic model is solved using the
+ function <code><a href='mkinpredict.html'>mkinpredict</a></code>. The variance of the residuals for each
+ observed variable can optionally be iteratively reweighted until convergence
+ using the argument <code>reweight.method = "obs"</code>.</p>
+
+ </div>
+
+ <div class="Value">
+ <h2>Value</h2>
+
+ <p><dl>
+ A list with "mkinfit" and "modFit" in the class attribute.
+ A summary can be obtained by <code><a href='summary.mkinfit.html'>summary.mkinfit</a></code>.
+</dl></p>
+
+ </div>
+
+ <div class="Note">
+ <h2>Note</h2>
+
+ <p>The implementation of iteratively reweighted least squares is inspired by the
+ work of the KinGUII team at Bayer Crop Science (Walter Schmitt and Zhenglei
+ Gao). A similar implemention can also be found in CAKE 2.0, which is the
+ other GUI derivative of mkin, sponsored by Syngenta.</p>
+
+ </div>
+
+ <div class="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>
+
+ <h2 id="examples">Examples</h2>
+ <pre class="examples"><div class='input'># Use shorthand notation for parent only degradation
+fit &lt;- mkinfit(&quot;FOMC&quot;, FOCUS_2006_C, quiet = TRUE)
+summary(fit)
+</div>
+<div class='output'>mkin version: 0.9.41
+R version: 3.2.2
+Date of fit: Mon Nov 9 08:25:21 2015
+Date of summary: Mon Nov 9 08:25:21 2015
+
+Equations:
+d_parent = - (alpha/beta) * 1/((time/beta) + 1) * parent
+
+Model predictions using solution type analytical
+
+Fitted with method Port using 64 model solutions performed in 0.18 s
+
+Weighting: none
+
+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
+
+Optimised, transformed parameters with symmetric confidence intervals:
+ Estimate Std. Error Lower Upper
+parent_0 85.87000 2.2460 80.38000 91.3700
+log_alpha 0.05192 0.1605 -0.34080 0.4446
+log_beta 0.65100 0.2801 -0.03452 1.3360
+
+Parameter correlation:
+ parent_0 log_alpha log_beta
+parent_0 1.0000 -0.2033 -0.3624
+log_alpha -0.2033 1.0000 0.9547
+log_beta -0.3624 0.9547 1.0000
+
+Residual standard error: 2.275 on 6 degrees of freedom
+
+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(&gt;t) Lower Upper
+parent_0 85.870 38.230 1.069e-08 80.3800 91.370
+alpha 1.053 6.231 3.953e-04 0.7112 1.560
+beta 1.917 3.570 5.895e-03 0.9661 3.806
+
+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'>
+# One parent compound, one metabolite, both single first order.
+# Use mkinsub for convenience in model formulation. Pathway to sink included per default.
+SFO_SFO &lt;- mkinmod(
+ parent = mkinsub(&quot;SFO&quot;, &quot;m1&quot;),
+ m1 = mkinsub(&quot;SFO&quot;))
+</div>
+<strong class='message'>Successfully compiled differential equation model from auto-generated C code.</strong>
+<div class='input'># Fit the model to the FOCUS example dataset D using defaults
+print(system.time(fit &lt;- mkinfit(SFO_SFO, FOCUS_2006_D,
+ solution_type = &quot;eigen&quot;, quiet = TRUE)))
+</div>
+<div class='output'> user system elapsed
+ 1.176 1.204 0.894
+</div>
+<div class='input'>coef(fit)
+</div>
+<div class='output'> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
+ 99.59848 -3.03822 -2.98030 -5.24750
+</div>
+<div class='input'>endpoints(fit)
+</div>
+<div class='output'>$ff
+parent_sink parent_m1 m1_sink
+ 0.485524 0.514476 1.000000
+
+$SFORB
+logical(0)
+
+$distimes
+ DT50 DT90
+parent 7.022929 23.32967
+m1 131.760712 437.69961
+
+</div>
+<div class='input'>## Not run:
+# # deSolve is slower when no C compiler (gcc) was available during model generation
+# print(system.time(fit.deSolve &lt;- mkinfit(SFO_SFO, FOCUS_2006_D,
+# solution_type = &quot;deSolve&quot;)))
+# coef(fit.deSolve)
+# endpoints(fit.deSolve)
+# ## End(Not run)
+
+# Use stepwise fitting, using optimised parameters from parent only fit, FOMC
+## Not run:
+# FOMC_SFO &lt;- mkinmod(
+# parent = mkinsub(&quot;FOMC&quot;, &quot;m1&quot;),
+# m1 = mkinsub(&quot;SFO&quot;))
+# # Fit the model to the FOCUS example dataset D using defaults
+# fit.FOMC_SFO &lt;- mkinfit(FOMC_SFO, FOCUS_2006_D)
+# # Use starting parameters from parent only FOMC fit
+# fit.FOMC = mkinfit(&quot;FOMC&quot;, FOCUS_2006_D, plot=TRUE)
+# fit.FOMC_SFO &lt;- mkinfit(FOMC_SFO, FOCUS_2006_D,
+# parms.ini = fit.FOMC$bparms.ode, plot=TRUE)
+#
+# # Use stepwise fitting, using optimised parameters from parent only fit, SFORB
+# SFORB_SFO &lt;- mkinmod(
+# parent = list(type = &quot;SFORB&quot;, to = &quot;m1&quot;, sink = TRUE),
+# m1 = list(type = &quot;SFO&quot;))
+# # Fit the model to the FOCUS example dataset D using defaults
+# fit.SFORB_SFO &lt;- mkinfit(SFORB_SFO, FOCUS_2006_D)
+# fit.SFORB_SFO.deSolve &lt;- mkinfit(SFORB_SFO, FOCUS_2006_D, solution_type = &quot;deSolve&quot;)
+# # Use starting parameters from parent only SFORB fit (not really needed in this case)
+# fit.SFORB = mkinfit(&quot;SFORB&quot;, FOCUS_2006_D)
+# fit.SFORB_SFO &lt;- mkinfit(SFORB_SFO, FOCUS_2006_D, parms.ini = fit.SFORB$bparms.ode)
+# ## End(Not run)
+
+## Not run:
+# # Weighted fits, including IRLS
+# SFO_SFO.ff &lt;- mkinmod(parent = mkinsub(&quot;SFO&quot;, &quot;m1&quot;),
+# m1 = mkinsub(&quot;SFO&quot;), use_of_ff = &quot;max&quot;)
+# f.noweight &lt;- mkinfit(SFO_SFO.ff, FOCUS_2006_D)
+# summary(f.noweight)
+# f.irls &lt;- mkinfit(SFO_SFO.ff, FOCUS_2006_D, reweight.method = &quot;obs&quot;)
+# summary(f.irls)
+# f.w.mean &lt;- mkinfit(SFO_SFO.ff, FOCUS_2006_D, weight = &quot;mean&quot;)
+# summary(f.w.mean)
+# f.w.mean.irls &lt;- mkinfit(SFO_SFO.ff, FOCUS_2006_D, weight = &quot;mean&quot;,
+# reweight.method = &quot;obs&quot;)
+# summary(f.w.mean.irls)
+# ## End(Not run)
+
+## Not run:
+# # Manual weighting
+# dw &lt;- FOCUS_2006_D
+# errors &lt;- c(parent = 2, m1 = 1)
+# dw$err.man &lt;- errors[FOCUS_2006_D$name]
+# f.w.man &lt;- mkinfit(SFO_SFO.ff, dw, err = &quot;err.man&quot;)
+# summary(f.w.man)
+# f.w.man.irls &lt;- mkinfit(SFO_SFO.ff, dw, err = &quot;err.man&quot;,
+# reweight.method = &quot;obs&quot;)
+# summary(f.w.man.irls)
+# ## End(Not run)
+</div></pre>
+ </div>
+ <div class="span4">
+ <!-- <ul>
+ <li>mkinfit</li>
+ </ul>
+ <ul>
+ <li> optimize </li>
+ </ul> -->
+
+ <h2>See also</h2>
+
+ Plotting methods <code><a href='plot.mkinfit.html'>plot.mkinfit</a></code> and
+ <code><a href='mkinparplot.html'>mkinparplot</a></code>.
+
+ Fitting of several models to several datasets in a single call to
+ <code><a href='mmkin.html'>mmkin</a></code>.
+
+
+ <h2>Author</h2>
+
+ Johannes Ranke
+
+
+ </div>
+</div>
+
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