mkinfit: Fit a kinetic model to data with one or more state variables

Description

This function maximises the likelihood of the observed data using the Port algorithm nlminb, and the specified initial or fixed parameters and starting values. In each step of the optimsation, the kinetic model is solved using the function mkinpredict. 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.

Per default, parameters in the kinetic models are internally transformed in order to better satisfy the assumption of a normal distribution of their estimators.

Usage

mkinfit(mkinmod, observed,
  parms.ini = "auto",
  state.ini = "auto",
  err.ini = "auto",
  fixed_parms = NULL, fixed_initials = names(mkinmod$diffs)[-1],
  from_max_mean = FALSE,
  solution_type = c("auto", "analytical", "eigen", "deSolve"),
  method.ode = "lsoda",
  use_compiled = "auto",
  control = list(eval.max = 300, iter.max = 200),
  transform_rates = TRUE,
  transform_fractions = TRUE,
  quiet = FALSE,
  atol = 1e-8, rtol = 1e-10, n.outtimes = 100,
  error_model = c("const", "obs", "tc"),
  error_model_algorithm = c("d_3", "direct", "twostep", "threestep", "fourstep", "IRLS"),
  reweight.tol = 1e-8, reweight.max.iter = 10,
  trace_parms = FALSE, ...)

Arguments

mkinmod

A list of class mkinmod, 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 observed.

observed

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.

parms.ini

A named vector of initial values for the parameters, including parameters to be optimised and potentially also fixed parameters as indicated by 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.

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 map component of mkinmod). 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.

err.ini

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.

fixed_parms

The names of parameters that should not be optimised but rather kept at the values specified in parms.ini.

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.

from_max_mean

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.

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 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 "deSolve" if a compiler is present, and "eigen" if no compiler is present and the model can be expressed using eigenvalues and eigenvectors. This argument is passed on to the helper function mkinpredict.

method.ode

The solution method passed via mkinpredict to ode in case the solution type is "deSolve". The default "lsoda" is performant, but sometimes fails to converge.

use_compiled

If set to FALSE, no compiled version of the mkinmod model is used in the calls to mkinpredict even if a compiled version is present.

control

A list of control arguments passed to nlminb.

transform_rates

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.

transform_fractions

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 ilr transformation.

quiet

Suppress printing out the current value of the negative log-likelihood after each improvement?

atol

Absolute error tolerance, passed to ode. Default is 1e-8, lower than in lsoda.

rtol

Absolute error tolerance, passed to ode. Default is 1e-10, much lower than in lsoda.

n.outtimes

The length of the dataseries that is produced by the model prediction function mkinpredict. This impacts the accuracy of the numerical solver if that is used (see solution_type argument. The default value is 100.

error_model

If the error model is "const", a constant standard deviation is assumed.

If the error model is "obs", each observed variable is assumed to have its own variance.

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.

error_model_algorithm

If the error model is "const", the error model algorithm is ignored, because no special algorithm is needed and unweighted (also known as ordinary) least squares fitting can be applied.

The default 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.

The algorithm "direct" will directly minimize the negative log-likelihood.

The algorithm "twostep" will minimize the negative log-likelihood after an initial unweighted least squares optimisation step.

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.

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.

The algorithm "IRLS" 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.

reweight.tol

Tolerance for the convergence criterion calculated from the error model parameters in IRLS fits.

reweight.max.iter

Maximum number of iterations in IRLS fits.

trace_parms

Should a trace of the parameter values be listed?

…

Further arguments that will be passed on to deSolve.

Value

A list with "mkinfit" in the class attribute. A summary can be obtained by summary.mkinfit.

Examples

Run this code

# NOT RUN {
# Use shorthand notation for parent only degradation
fit <- mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE)
summary(fit)

# One parent compound, one metabolite, both single first order.
# Use mkinsub for convenience in model formulation. Pathway to sink included per default.
SFO_SFO <- mkinmod(
  parent = mkinsub("SFO", "m1"),
  m1 = mkinsub("SFO"))
# Fit the model to the FOCUS example dataset D using defaults
print(system.time(fit <- mkinfit(SFO_SFO, FOCUS_2006_D,
                           solution_type = "eigen", quiet = TRUE)))
coef(fit)
endpoints(fit)
# }
# NOT RUN {
# deSolve is slower when no C compiler (gcc) was available during model generation
print(system.time(fit.deSolve <- mkinfit(SFO_SFO, FOCUS_2006_D,
                           solution_type = "deSolve")))
coef(fit.deSolve)
endpoints(fit.deSolve)
# }
# NOT RUN {
# Use stepwise fitting, using optimised parameters from parent only fit, FOMC
# }
# NOT RUN {
FOMC_SFO <- mkinmod(
  parent = mkinsub("FOMC", "m1"),
  m1 = mkinsub("SFO"))
# Fit the model to the FOCUS example dataset D using defaults
fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE)
# Use starting parameters from parent only FOMC fit
fit.FOMC = mkinfit("FOMC", FOCUS_2006_D, quiet = TRUE)
fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE,
  parms.ini = fit.FOMC$bparms.ode)

# Use stepwise fitting, using optimised parameters from parent only fit, 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, quiet = TRUE)
fit.SFORB_SFO.deSolve <- mkinfit(SFORB_SFO, FOCUS_2006_D, solution_type = "deSolve",
                                 quiet = TRUE)
# Use starting parameters from parent only SFORB fit (not really needed in this case)
fit.SFORB = mkinfit("SFORB", FOCUS_2006_D, quiet = TRUE)
fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D, parms.ini = fit.SFORB$bparms.ode, quiet = TRUE)
# }
# NOT RUN {
# }
# NOT RUN {
# Weighted fits, including IRLS
SFO_SFO.ff <- mkinmod(parent = mkinsub("SFO", "m1"),
                      m1 = mkinsub("SFO"), use_of_ff = "max")
f.noweight <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, quiet = TRUE)
summary(f.noweight)
f.obs <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, error_model = "obs", quiet = TRUE)
summary(f.obs)
f.tc <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, error_model = "tc", quiet = TRUE)
summary(f.tc)
# }
# NOT RUN {
# }

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Description

Usage

Arguments

Value

See Also

Examples