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. 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. 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. 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. 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 datafit.s <- summary(fit)
# Transformed and backtransformed parameters
print(fit.s$par, 3)#> Estimate Std. Error Lower Upper #> parent_0 99.60 1.5702 96.40 102.79 #> log_k_parent_sink -3.04 0.0763 -3.19 -2.88 #> log_k_parent_m1 -2.98 0.0403 -3.06 -2.90 #> log_k_m1_sink -5.25 0.1332 -5.52 -4.98 #> sigma 3.13 0.3585 2.40 3.85print(fit.s$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_sink  0.04792    0.00365   13.11 6.13e-15  0.04103   0.0560
#> k_parent_m1    0.05078    0.00205   24.80 3.27e-23  0.04678   0.0551
#> k_m1_sink      0.00526    0.00070    7.51 6.16e-09  0.00401   0.0069
#> 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 datafit.2.s <- summary(fit.2)
print(fit.2.s$par, 3)#> Estimate Std. Error Lower Upper #> parent_0 99.59848 1.57022 96.40384 1.03e+02 #> k_parent_sink 0.04792 0.00365 0.04049 5.54e-02 #> k_parent_m1 0.05078 0.00205 0.04661 5.49e-02 #> k_m1_sink 0.00526 0.00070 0.00384 6.69e-03 #> sigma 3.12550 0.35852 2.39609 3.85e+00print(fit.2.s$bpar, 3)#>               Estimate se_notrans t value   Pr(>t)    Lower    Upper
#> parent_0      99.59848    1.57022   63.43 2.30e-36 96.40384 1.03e+02
#> k_parent_sink  0.04792    0.00365   13.11 6.13e-15  0.04049 5.54e-02
#> k_parent_m1    0.05078    0.00205   24.80 3.27e-23  0.04661 5.49e-02
#> k_m1_sink      0.00526    0.00070    7.51 6.16e-09  0.00384 6.69e-03
#> sigma          3.12550    0.35852    8.72 2.24e-10  2.39609 3.85e+00# }

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_sink   log_k_parent_m1     log_k_m1_sink
#>        100.750000         -2.302585         -2.301586         -2.300587 backtransform_odeparms(transformed, SFO_SFO)#>      parent_0 k_parent_sink   k_parent_m1     k_m1_sink
#>      100.7500        0.1000        0.1001        0.1002
# \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 datafit.ff.s <- summary(fit.ff)
print(fit.ff.s$par, 3)#> Estimate Std. Error Lower Upper #> parent_0 99.598 1.5702 96.4038 102.793 #> log_k_parent -2.316 0.0409 -2.3988 -2.233 #> log_k_m1 -5.248 0.1332 -5.5184 -4.977 #> f_parent_ilr_1 0.041 0.0631 -0.0875 0.169 #> sigma 3.126 0.3585 2.3961 3.855print(fit.ff.s$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   3.8549initials <- 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 datafit.ff.2.s <- summary(fit.ff.2)
print(fit.ff.2.s$par, 3)#> Estimate Std. Error Lower Upper #> parent_0 84.79 3.012 78.67 90.91 #> log_k_parent -2.76 0.082 -2.92 -2.59 #> log_k_m1 -4.21 0.123 -4.46 -3.96 #> sigma 8.22 0.943 6.31 10.14print(fit.ff.2.s$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# }