mkinfit {mkin} | R Documentation |
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.
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, ...)
mkinmod |
A list of class |
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
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 |
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 |
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
|
method.ode |
The solution method passed via |
use_compiled |
If set to |
control |
A list of control arguments passed to |
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
|
quiet |
Suppress printing out the current value of the negative log-likelihood after each improvement? |
atol |
Absolute error tolerance, passed to |
rtol |
Absolute error tolerance, passed to |
n.outtimes |
The length of the dataseries that is produced by the model prediction
function |
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 |
A list with "mkinfit" in the class attribute. A summary can be obtained by
summary.mkinfit
.
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.
Johannes Ranke
Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for measurement error in analytical chemistry. Technometrics 37(2), 176-184.
Plotting methods plot.mkinfit
and mkinparplot
.
Comparisons of models fitted to the same data can be made using AIC
by virtue of the method logLik.mkinfit
.
Fitting of several models to several datasets in a single call to
mmkin
.
# 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) ## End(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) ## End(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) ## End(Not run)