\name{mkinfit}
\alias{mkinfit}
\title{
  Fit a kinetic model to data with one or more state variables.
}
\description{
  This function uses the Flexible Modelling Environment package
  \code{\link{FME}} 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 Levenberg-Marquardt algorithm \code{\link{nls.lm}}, 
  using the specified initial or fixed parameters and starting values.
  In each step of the optimsation, the kinetic model is solved using the
  function \code{\link{mkinpredict}}. The variance of the residuals for each
  observed variable can optionally be iteratively reweighted until convergence
  using the argument \code{reweight.method = "obs"}.
}
\usage{
mkinfit(mkinmod, observed, 
  parms.ini = "auto",
  state.ini = c(100, rep(0, length(mkinmod$diffs) - 1)), 
  fixed_parms = NULL, fixed_initials = names(mkinmod$diffs)[-1], 
  solution_type = "auto",
  method.modFit = "Marq",
  control.modFit = list(),
  plot = FALSE, quiet = FALSE, err = NULL, weight = "none", 
  scaleVar = FALSE, 
  atol = 1e-8, rtol = 1e-10, n.outtimes = 100, 
  reweight.method = NULL,
  reweight.tol = 1e-8, reweight.max.iter = 10,
  trace_parms = FALSE, ...)
}
\arguments{
  \item{mkinmod}{
    A list of class \code{\link{mkinmod}}, containing the kinetic model to be fitted to the data.
  }
  \item{observed}{
    The observed data. It has to be in the long format as described in
    \code{\link{modFit}}, 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} which is then passed
    on to \code{\link{modFit}}.
  }
  \item{parms.ini}{
    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}.  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.
  }
  \item{state.ini}{
    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} component of \code{\link{mkinmod}}). The default is to set
    the initial value of the first model variable to 100 and all others to 0.
  }
  \item{fixed_parms}{
    The names of parameters that should not be optimised but rather kept at the
    values specified in \code{parms.ini}.
  }
  \item{fixed_initials}{
    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.
  }
  \item{solution_type}{
    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{\link{deSolve}} 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{\link{mkinpredict}}.
  }
  \item{method.modFit}{
    The optimisation method passed to \code{\link{modFit}}. The default "Marq"
    is the Levenberg Marquardt algorithm \code{\link{nls.lm}} from the package
    \code{minpack.lm}. Often other methods need more iterations to find the
    same result. When using "Pseudo", "upper" and "lower" need to be 
    specified for the transformed parameters.
  }
  \item{control.modFit}{
    Additional arguments passed to the optimisation method used by
    \code{\link{modFit}}.
  }
  \item{plot}{
    Should the observed values and the numerical solutions be plotted at each
    stage of the optimisation?
  }
  \item{quiet}{
    Suppress printing out the current model cost after each improvement?
  }
  \item{err }{either \code{NULL}, or the name of the column with the
    \emph{error} estimates, used to weigh the residuals (see details of
    \code{\link{modCost}}); if \code{NULL}, then the residuals are not weighed.
  }
  \item{weight}{
    only if \code{err}=\code{NULL}: how to weight the residuals, one of "none",
    "std", "mean", see details of \code{\link{modCost}}.
  }
  \item{scaleVar}{
    Will be passed to \code{\link{modCost}}. Default is not to scale Variables
    according to the number of observations.
  }
  \item{atol}{
    Absolute error tolerance, passed to \code{\link{ode}}. Default is 1e-8,
    lower than in \code{\link{lsoda}}.
  }
  \item{rtol}{
    Absolute error tolerance, passed to \code{\link{ode}}. Default is 1e-10,
    much lower than in \code{\link{lsoda}}.
  }
  \item{n.outtimes}{
    The length of the dataseries that is produced by the model prediction
    function \code{\link{mkinpredict}}. This impacts the accuracy of
    the numerical solver if that is used (see \code{solution_type} argument. 
    The default value is 100.
  }
  \item{reweight.method}{
    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} or up to the maximum number of iterations
    specified by \code{reweight.max.iter}.
  }
  \item{reweight.tol}{
    Tolerance for convergence criterion for the variance components
    in IRLS fits.
  }
  \item{reweight.max.iter}{
    Maximum iterations in IRLS fits.
  }
  \item{trace_parms}{
    Should a trace of the parameter values be listed?
  }
  \item{\dots}{
    Further arguments that will be passed to \code{\link{modFit}}. 
  }
}
\value{
  A list with "mkinfit" and "modFit" in the class attribute. 
  A summary can be obtained by \code{\link{summary.mkinfit}}. 
}
\note{
  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.
}
\author{
  Johannes Ranke <jranke@uni-bremen.de>
}
\examples{
# One parent compound, one metabolite, both single first order.
SFO_SFO <- mkinmod(
  parent = list(type = "SFO", to = "m1", sink = TRUE),
  m1 = list(type = "SFO"))
# Fit the model to the FOCUS example dataset D using defaults
fit <- mkinfit(SFO_SFO, FOCUS_2006_D)
summary(fit)

# Use stepwise fitting, using optimised parameters from parent only fit, FOMC
\dontrun{
FOMC <- mkinmod(parent = list(type = "FOMC"))
FOMC_SFO <- mkinmod(
  parent = list(type = "FOMC", to = "m1", sink = TRUE),
  m1 = list(type = "SFO"))
# Fit the model to the FOCUS example dataset D using defaults
fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D)
# Use starting parameters from parent only FOMC fit
fit.FOMC = mkinfit(FOMC, FOCUS_2006_D, plot=TRUE)
fit.FOMC_SFO <- 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 <- mkinmod(parent = list(type = "SFORB"))
SFORB_SFO <- mkinmod(
  parent = list(type = "SFORB", to = "m1", sink = TRUE),
  m1 = list(type = "SFO"))
# Fit the model to the FOCUS example dataset D using defaults
fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D)
# Use starting parameters from parent only SFORB fit (not really needed in this case)
fit.SFORB = mkinfit(SFORB, FOCUS_2006_D)
fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D, parms.ini = fit.SFORB$bparms.ode)
}

# Weighted fits, including IRLS
SFO_SFO.ff <- mkinmod(parent = list(type = "SFO", to = "m1"),
                      m1 = list(type = "SFO"), use_of_ff = "max")
f.noweight <- mkinfit(SFO_SFO.ff, FOCUS_2006_D)
summary(f.noweight)
f.irls <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, reweight.method = "obs")
summary(f.irls)
f.w.mean <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, weight = "mean")
summary(f.w.mean)
f.w.mean.irls <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, weight = "mean",
                         reweight.method = "obs")
summary(f.w.mean.irls)

\dontrun{
# Manual weighting
dw <- FOCUS_2006_D
errors <- c(parent = 2, m1 = 1)
dw$err.man <- errors[FOCUS_2006_D$name]
f.w.man <- mkinfit(SFO_SFO.ff, dw, err = "err.man")
summary(f.w.man)
f.w.man.irls <- mkinfit(SFO_SFO.ff, dw, err = "err.man",
                       reweight.method = "obs")
summary(f.w.man.irls)
}
}
\keyword{ models }
\keyword{ optimize }