The transformations are intended to map parameters that should only take on restricted values to the full scale of real numbers. For kinetic rate constants and other paramters that can only take on positive values, a simple log transformation is used. For compositional parameters, such as the formations fractions that should always sum up to 1 and can not be negative, the ilr transformation is used.

transform_odeparms(
  parms,
  mkinmod,
  transform_rates = TRUE,
  transform_fractions = TRUE
)

backtransform_odeparms(
  transparms,
  mkinmod,
  transform_rates = TRUE,
  transform_fractions = TRUE
)

Arguments

parms

Parameters of kinetic models as used in the differential equations.

mkinmod

The kinetic model of class mkinmod, containing the names of the model variables that are needed for grouping the formation fractions before ilr transformation, the parameter names and the information if the pathway to sink is included in the model.

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.

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. 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.

transparms

Transformed parameters of kinetic models as used in the fitting procedure.

Value

A vector of transformed or backtransformed parameters with the same names as the original parameters.

Details

The transformation of sets of formation fractions is fragile, as it supposes the same ordering of the components in forward and backward transformation. This is no problem for the internal use in mkinfit.

Functions

  • backtransform_odeparms: Backtransform the set of transformed parameters

Examples

SFO_SFO <- mkinmod( parent = list(type = "SFO", to = "m1", sink = TRUE), m1 = list(type = "SFO"))
#> Successfully compiled differential equation model from auto-generated C code.
# Fit the model to the FOCUS example dataset D using defaults fit <- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
fit.s <- summary(fit) # Transformed and backtransformed parameters print(fit.s$par, 3)
#> Estimate Std. Error Lower Upper #> parent_0 99.598 1.5702 96.4038 102.793 #> log_k_parent -2.316 0.0409 -2.3988 -2.233 #> log_k_m1 -5.248 0.1332 -5.5184 -4.977 #> f_parent_ilr_1 0.041 0.0631 -0.0875 0.169 #> sigma 3.126 0.3585 2.3961 3.855
print(fit.s$bpar, 3)
#> Estimate se_notrans t value Pr(>t) Lower Upper #> parent_0 99.59848 1.57022 63.43 2.30e-36 96.40384 102.7931 #> k_parent 0.09870 0.00403 24.47 4.96e-23 0.09082 0.1073 #> k_m1 0.00526 0.00070 7.51 6.16e-09 0.00401 0.0069 #> f_parent_to_m1 0.51448 0.02230 23.07 3.10e-22 0.46912 0.5596 #> sigma 3.12550 0.35852 8.72 2.24e-10 2.39609 3.8549
# \dontrun{ # Compare to the version without transforming rate parameters fit.2 <- mkinfit(SFO_SFO, FOCUS_2006_D, transform_rates = FALSE, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
#> Error in if (cost < cost.current) { assign("cost.current", cost, inherits = TRUE) if (!quiet) cat(ifelse(OLS, "Sum of squared residuals", "Negative log-likelihood"), " at call ", calls, ": ", cost.current, "\n", sep = "")}: Fehlender Wert, wo TRUE/FALSE nötig ist
#> Timing stopped at: 0.002 0 0.003
fit.2.s <- summary(fit.2)
#> Error in summary(fit.2): Objekt 'fit.2' nicht gefunden
print(fit.2.s$par, 3)
#> Error in print(fit.2.s$par, 3): Objekt 'fit.2.s' nicht gefunden
print(fit.2.s$bpar, 3)
#> Error in print(fit.2.s$bpar, 3): Objekt 'fit.2.s' nicht gefunden
# } initials <- fit$start$value names(initials) <- rownames(fit$start) transformed <- fit$start_transformed$value names(transformed) <- rownames(fit$start_transformed) transform_odeparms(initials, SFO_SFO)
#> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 #> 100.750000 -2.302585 -2.301586 0.000000
backtransform_odeparms(transformed, SFO_SFO)
#> parent_0 k_parent k_m1 f_parent_to_m1 #> 100.7500 0.1000 0.1001 0.5000
# \dontrun{ # The case of formation fractions SFO_SFO.ff <- mkinmod( parent = list(type = "SFO", to = "m1", sink = TRUE), m1 = list(type = "SFO"), use_of_ff = "max")
#> Successfully compiled differential equation model from auto-generated C code.
fit.ff <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
fit.ff.s <- summary(fit.ff) print(fit.ff.s$par, 3)
#> Estimate Std. Error Lower Upper #> parent_0 99.598 1.5702 96.4038 102.793 #> log_k_parent -2.316 0.0409 -2.3988 -2.233 #> log_k_m1 -5.248 0.1332 -5.5184 -4.977 #> f_parent_ilr_1 0.041 0.0631 -0.0875 0.169 #> sigma 3.126 0.3585 2.3961 3.855
print(fit.ff.s$bpar, 3)
#> Estimate se_notrans t value Pr(>t) Lower Upper #> parent_0 99.59848 1.57022 63.43 2.30e-36 96.40384 102.7931 #> k_parent 0.09870 0.00403 24.47 4.96e-23 0.09082 0.1073 #> k_m1 0.00526 0.00070 7.51 6.16e-09 0.00401 0.0069 #> f_parent_to_m1 0.51448 0.02230 23.07 3.10e-22 0.46912 0.5596 #> sigma 3.12550 0.35852 8.72 2.24e-10 2.39609 3.8549
initials <- c("f_parent_to_m1" = 0.5) transformed <- transform_odeparms(initials, SFO_SFO.ff) backtransform_odeparms(transformed, SFO_SFO.ff)
#> f_parent_to_m1 #> 0.5
# And without sink SFO_SFO.ff.2 <- mkinmod( parent = list(type = "SFO", to = "m1", sink = FALSE), m1 = list(type = "SFO"), use_of_ff = "max")
#> Successfully compiled differential equation model from auto-generated C code.
fit.ff.2 <- mkinfit(SFO_SFO.ff.2, FOCUS_2006_D, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
fit.ff.2.s <- summary(fit.ff.2) print(fit.ff.2.s$par, 3)
#> Estimate Std. Error Lower Upper #> parent_0 84.79 3.012 78.67 90.91 #> log_k_parent -2.76 0.082 -2.92 -2.59 #> log_k_m1 -4.21 0.123 -4.46 -3.96 #> sigma 8.22 0.943 6.31 10.14
print(fit.ff.2.s$bpar, 3)
#> Estimate se_notrans t value Pr(>t) Lower Upper #> parent_0 84.7916 3.01203 28.15 1.92e-25 78.6704 90.913 #> k_parent 0.0635 0.00521 12.19 2.91e-14 0.0538 0.075 #> k_m1 0.0148 0.00182 8.13 8.81e-10 0.0115 0.019 #> sigma 8.2229 0.94323 8.72 1.73e-10 6.3060 10.140
# }