This function uses the Flexible Modelling Environment package
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 Port algorithm nlminb,
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 mkinpredict. The variance of the residuals for each
observed variable can optionally be iteratively reweighted until convergence
using the argument reweight.method = "obs".
mkinfit(mkinmod, observed, parms.ini = "auto", state.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", method.modFit = c("Port", "Marq", "SANN", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B"), maxit.modFit = "auto", control.modFit = list(), transform_rates = TRUE, transform_fractions = TRUE, 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, ...)
mkinmod, 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
observed.
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. Its name must be passed as a
further argument named err which is then passed on to
modFit.
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.
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.
parms.ini.
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 mkinpredict.
mkinpredict to
ode in case the solution type is "deSolve". The default
"lsoda" is performant, but sometimes fails to converge.
FALSE, no compiled version of the mkinmod
model is used, in the calls to mkinpredict even if
a compiled verion is present.
modFit.
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
nls.lm from the package minpack.lm 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 control.modFit and it does not appear
to provide advantages over the other algorithms.
modFit, overriding
what may be specified in the next argument control.modFit.
modFit.
ilr transformation.
NULL, or the name of the column with the
error estimates, used to weigh the residuals (see details of
modCost); if NULL, then the residuals are not weighed.
err=NULL: how to weight the residuals, one of "none",
"std", "mean", see details of modCost.
modCost. Default is not to scale Variables
according to the number of observations.
ode. Default is 1e-8,
lower than in lsoda.
ode. Default is 1e-10,
much lower than in lsoda.
mkinpredict. This impacts the accuracy of
the numerical solver if that is used (see solution_type argument.
The default value is 100.
reweight.tol or up to the maximum number of iterations
specified by reweight.max.iter.
modFit.
A list with "mkinfit" and "modFit" in the class attribute.
A summary can be obtained by summary.mkinfit.
Plotting methods plot.mkinfit and
mkinparplot.
Fitting of several models to several datasets in a single call to
mmkin.
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.
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.
# Use shorthand notation for parent only degradation fit <- mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE) summary(fit)#> mkin version: 0.9.44.9000 #> R version: 3.3.1 #> Date of fit: Thu Oct 6 10:47:36 2016 #> Date of summary: Thu Oct 6 10:47:36 2016 #> #> 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 0.152 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(>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 #># 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"))Successfully compiled differential equation model from auto-generated C code.# 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)))#> user system elapsed #> 1.240 1.280 0.973 #>coef(fit)#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink #> 99.59848 -3.03822 -2.98030 -5.24750 #>endpoints(fit)#> $ff #> parent_sink parent_m1 m1_sink #> 0.485524 0.514476 1.000000 #> #> $SFORB #> logical(0) #> #> $distimes #> DT50 DT90 #> parent 7.022929 23.32967 #> m1 131.760712 437.69961 #> #>## Not run: ------------------------------------ # # deSolve is slower when no C compiler (gcc) was available during model generation # print(system.time(fit.deSolve <- mkinfit(SFO_SFO, FOCUS_2006_D, # solution_type = "deSolve"))) # coef(fit.deSolve) # endpoints(fit.deSolve) ## --------------------------------------------- # Use stepwise fitting, using optimised parameters from parent only fit, FOMC ## Not run: ------------------------------------ # FOMC_SFO <- mkinmod( # parent = mkinsub("FOMC", "m1"), # m1 = mkinsub("SFO")) # # Fit the model to the FOCUS example dataset D using defaults # fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D) # # Use starting parameters from parent only FOMC fit # fit.FOMC = mkinfit("FOMC", FOCUS_2006_D, plot=TRUE) # fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, # parms.ini = fit.FOMC$bparms.ode, plot=TRUE) # # # Use stepwise fitting, using optimised parameters from parent only fit, SFORB # SFORB_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) # fit.SFORB_SFO.deSolve <- mkinfit(SFORB_SFO, FOCUS_2006_D, solution_type = "deSolve") # # 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$bparms.ode) ## --------------------------------------------- ## Not run: ------------------------------------ # # Weighted fits, including IRLS # SFO_SFO.ff <- mkinmod(parent = mkinsub("SFO", "m1"), # m1 = mkinsub("SFO"), use_of_ff = "max") # f.noweight <- mkinfit(SFO_SFO.ff, FOCUS_2006_D) # summary(f.noweight) # f.irls <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, reweight.method = "obs") # summary(f.irls) # f.w.mean <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, weight = "mean") # summary(f.w.mean) # f.w.value <- mkinfit(SFO_SFO.ff, subset(FOCUS_2006_D, value != 0), err = "value") # summary(f.w.value) ## --------------------------------------------- ## Not run: ------------------------------------ # # Manual weighting # dw <- FOCUS_2006_D # errors <- c(parent = 2, m1 = 1) # dw$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) ## ---------------------------------------------