# Functions to transform and backtransform kinetic parameters for fitting

### Description

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.

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`

.

### Usage

1 2 3 4 | ```
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. |

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

`mkinmod` |
The kinetic model of class |

`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 |

### Value

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

### Author(s)

Johannes Ranke

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | ```
SFO_SFO <- mkinmod(
parent = list(type = "SFO", to = "m1", sink = TRUE),
m1 = list(type = "SFO"))
# Fit the model to the FOCUS example dataset D using defaults
fit <- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE)
summary(fit, data=FALSE) # See transformed and backtransformed parameters
## Not run:
fit.2 <- mkinfit(SFO_SFO, FOCUS_2006_D, transform_rates = FALSE)
summary(fit.2, data=FALSE)
## End(Not run)
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)
backtransform_odeparms(transformed, SFO_SFO)
## Not run:
# 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")
fit.ff <- mkinfit(SFO_SFO.ff, FOCUS_2006_D)
summary(fit.ff, data = FALSE)
initials <- c("f_parent_to_m1" = 0.5)
transformed <- transform_odeparms(initials, SFO_SFO.ff)
backtransform_odeparms(transformed, SFO_SFO.ff)
# And without sink
SFO_SFO.ff.2 <- mkinmod(
parent = list(type = "SFO", to = "m1", sink = FALSE),
m1 = list(type = "SFO"),
use_of_ff = "max")
fit.ff.2 <- mkinfit(SFO_SFO.ff.2, FOCUS_2006_D)
summary(fit.ff.2, data = FALSE)
## End(Not run)
``` |