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", "NelderMead", "BFGS", "CG", "LBFGSB"), maxit.modFit = "auto", control.modFit = list(), transform_rates = TRUE, transform_fractions = TRUE, plot = FALSE, quiet = FALSE, err = NULL, weight = c("none", "std", "mean", "tc"), tc = c(sigma_low = 0.5, rsd_high = 0.07), scaleVar = FALSE, atol = 1e8, rtol = 1e10, n.outtimes = 100, reweight.method = NULL, reweight.tol = 1e8, reweight.max.iter = 10, trace_parms = FALSE, ...)
mkinmod  A list of class 

observed  The observed data. It has to be in the long format as described in

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 
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 
method.modFit  The optimisation method passed to 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
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 
maxit.modFit  Maximum number of iterations in the optimisation. If not "auto", this will
be passed to the method called by 
control.modFit  Additional arguments passed to the optimisation method used by

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 logtransformed, 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

plot  Should the observed values and the numerical solutions be plotted at each stage of the optimisation? 
quiet  Suppress printing out the current model cost after each improvement? 
err  either 
weight  only if 
tc  The two components of the Rocke and Lorenzato error model as used for (initial) weighting 
scaleVar  Will be passed to 
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 
reweight.method  The method used for iteratively reweighting residuals, also known
as iteratively reweighted least squares (IRLS). Default is NULL,
i.e. no iterative weighting.
The first reweighting method is called "obs", meaning that each
observed variable is assumed to have its own variance. This variance
is estimated from the fit (mean squared residuals) and used for weighting
the residuals in each iteration until convergence of this estimate up to

reweight.tol  Tolerance for convergence criterion for the variance components in IRLS fits. 
reweight.max.iter  Maximum iterations in IRLS fits. 
trace_parms  Should a trace of the parameter values be listed? 
…  Further arguments that will be passed to 
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.
Rocke, David M. und Lorenzato, Stefan (1995) A twocomponent model for measurement error in analytical chemistry. Technometrics 37(2), 176184.
# Use shorthand notation for parent only degradation fit < mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE) summary(fit)#> mkin version used for fitting: 0.9.47.1 #> R version used for fitting: 3.4.3 #> Date of fit: Sun Mar 11 22:10:32 2018 #> Date of summary: Sun Mar 11 22:10:32 2018 #> #> Equations: #> d_parent/dt =  (alpha/beta) * 1/((time/beta) + 1) * parent #> #> Model predictions using solution type analytical #> #> Fitted with method Port using 64 model solutions performed in 0.135 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. #> ttest (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 1.069e08 80.3800 91.370 #> alpha 1.053 6.231 3.953e04 0.7112 1.560 #> beta 1.917 3.570 5.895e03 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"))#># 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 #> 0.829 0.000 0.829coef(fit)#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink #> 99.59848 3.03822 2.98030 5.24750endpoints(fit)#> $ff #> parent_sink parent_m1 m1_sink #> 0.485524 0.514476 1.000000 #> #> $SFORB #> logical(0) #> #> $distimes #> DT50 DT90 #> parent 7.022929 23.32967 #> m1 131.760712 437.69961 #># NOT RUN { # deSolve is slower when no C compiler (gcc) was available during model generation print(system.time(fit.deSolve < mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve"))) coef(fit.deSolve) endpoints(fit.deSolve) # }# Use stepwise fitting, using optimised parameters from parent only fit, FOMC# NOT RUN { FOMC_SFO < mkinmod( parent = mkinsub("FOMC", "m1"), m1 = mkinsub("SFO")) # Fit the model to the FOCUS example dataset D using defaults fit.FOMC_SFO < mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE) # Use starting parameters from parent only FOMC fit fit.FOMC = mkinfit("FOMC", FOCUS_2006_D, quiet = TRUE) fit.FOMC_SFO < mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE, parms.ini = fit.FOMC$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$bparms.ode, quiet = TRUE) # }# NOT RUN { # Weighted fits, including IRLS SFO_SFO.ff < mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"), use_of_ff = "max") f.noweight < mkinfit(SFO_SFO.ff, FOCUS_2006_D, quiet = TRUE) summary(f.noweight) f.irls < mkinfit(SFO_SFO.ff, FOCUS_2006_D, reweight.method = "obs", quiet = TRUE) summary(f.irls) f.w.mean < mkinfit(SFO_SFO.ff, FOCUS_2006_D, weight = "mean", quiet = TRUE) summary(f.w.mean) f.w.value < mkinfit(SFO_SFO.ff, subset(FOCUS_2006_D, value != 0), err = "value", quiet = TRUE) summary(f.w.value) # }# NOT RUN { # Manual weighting dw < FOCUS_2006_D errors < c(parent = 2, m1 = 1) dw$err.man < errors[FOCUS_2006_D$name] f.w.man < mkinfit(SFO_SFO.ff, dw, err = "err.man", quiet = TRUE) summary(f.w.man) f.w.man.irls < mkinfit(SFO_SFO.ff, dw, err = "err.man", quiet = TRUE, reweight.method = "obs") summary(f.w.man.irls) # }