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


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, ...)


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"). If a shorthand name is given, a parent only degradation model is generated for the variable with the highest value in observed.
The observed data. It has to be in the long format as described in 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.
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.
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.
The names of parameters that should not be optimised but rather kept at the values specified in parms.ini.
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.
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.
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 "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.
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.
If set to FALSE, no compiled version of the mkinmod model is used, in the calls to mkinpredict even if a compiled verion is present.
The optimisation method passed to 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.
Maximum number of iterations in the optimisation. If not "auto", this will be passed to the method called by modFit, overriding what may be specified in the next argument control.modFit.
Additional arguments passed to the optimisation method used by modFit.
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.
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.
Should the observed values and the numerical solutions be plotted at each stage of the optimisation?
Suppress printing out the current model cost after each improvement?
either 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.
only if err=NULL: how to weight the residuals, one of "none", "std", "mean", see details of modCost.
Will be passed to modCost. Default is not to scale Variables according to the number of observations.
Absolute error tolerance, passed to ode. Default is 1e-8, lower than in lsoda.
Absolute error tolerance, passed to ode. Default is 1e-10, much lower than in lsoda.
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.
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 reweight.tol or up to the maximum number of iterations specified by reweight.max.iter.
Tolerance for convergence criterion for the variance components in IRLS fits.
Maximum iterations in IRLS fits.
Should a trace of the parameter values be listed?
Further arguments that will be passed to modFit.


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".


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


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 R version: 3.3.1 Date of fit: Tue Jun 28 10:25:14 2016 Date of summary: Tue Jun 28 10:25:14 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 0.44 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 2.852 2.240 2.272
parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink 99.59848 -3.03822 -2.98030 -5.24750
$ff parent_sink parent_m1 m1_sink 0.485524 0.514476 1.000000 $SFORB logical(0) $distimes DT50 DT90 parent 7.022929 23.32967 m1 131.760712 437.69961
## Not run: # # deSolve is slower when no C compiler (gcc) was available during model generation # print(system.time(fit.deSolve <- mkinfit(SFO_SFO, FOCUS_2006_D, # solution_type = "deSolve"))) # coef(fit.deSolve) # endpoints(fit.deSolve) # ## End(Not run) # Use stepwise fitting, using optimised parameters from parent only fit, FOMC ## Not run: # FOMC_SFO <- mkinmod( # parent = mkinsub("FOMC", "m1"), # m1 = mkinsub("SFO")) # # Fit the model to the FOCUS example dataset D using defaults # fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D) # # Use starting parameters from parent only FOMC fit # fit.FOMC = mkinfit("FOMC", FOCUS_2006_D, plot=TRUE) # fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, # parms.ini = fit.FOMC$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$bparms.ode) # ## End(Not run) ## Not run: # # Weighted fits, including IRLS # SFO_SFO.ff <- mkinmod(parent = mkinsub("SFO", "m1"), # m1 = mkinsub("SFO"), use_of_ff = "max") # f.noweight <- mkinfit(SFO_SFO.ff, FOCUS_2006_D) # summary(f.noweight) # f.irls <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, reweight.method = "obs") # summary(f.irls) # f.w.mean <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, weight = "mean") # summary(f.w.mean) # f.w.value <- mkinfit(SFO_SFO.ff, subset(FOCUS_2006_D, value != 0), err = "value") # summary(f.w.value) # ## End(Not run) ## Not run: # # Manual weighting # dw <- FOCUS_2006_D # errors <- c(parent = 2, m1 = 1) # dw$ <- errors[FOCUS_2006_D$name] # <- mkinfit(SFO_SFO.ff, dw, err = "") # summary( # <- mkinfit(SFO_SFO.ff, dw, err = "", # reweight.method = "obs") # summary( # ## End(Not run)

See also

Plotting methods plot.mkinfit and mkinparplot. Fitting of several models to several datasets in a single call to mmkin.


Johannes Ranke