ctm: Conditional Transformation Models
In mlt: Most Likely Transformations

ctm	R Documentation

Conditional Transformation Models

Description

Specification of conditional transformation models

Usage

ctm(response, interacting = NULL, shifting = NULL, scaling = NULL, 
    scale_shift = FALSE, data = NULL, 
    todistr = c("Normal", "Logistic", "MinExtrVal", "MaxExtrVal", 
                "Exponential", "Laplace", "Cauchy"), 
    sumconstr = inherits(interacting, c("formula", "formula_basis")), ...)
has_scale(object)

Arguments

`response`	a basis function, ie, an object of class `basis`
`interacting`	a basis function, ie, an object of class `basis`
`shifting`	a basis function, ie, an object of class `basis`
`scaling`	a basis function, ie, an object of class `basis`
`scale_shift`	a logical choosing between two different model types in the presence of a `scaling` term
`data`	either a `data.frame` containing the model variables or a formal description of these variables in an object of class `vars`
`todistr`	a character vector describing the distribution to be transformed
`sumconstr`	a logical indicating if sum constraints shall be applied
`object`	an object of class `ctm`
`...`	arguments to `as.basis` when `shifting` is a formula

Details

This function only specifies the model which can then be fitted using mlt. The shift term is positive by default. All arguments except response can be missing (in this case an unconditional distribution is estimated). \bibcitetmlt::Hothorn:Moest:Buehlmann:2017 explain the model class.

Possible choices of the distributions the model transforms to (the inverse link functions F_Z) include the standard normal ("Normal"), the standard logistic ("Logistic"), the standard minimum extreme value ("MinExtrVal", also known as Gompertz distribution), and the standard maximum extreme value ("MaxExtrVal", also known as Gumbel distribution) distributions. The exponential distribution ("Exponential") can be used to fit Aalen additive hazard models. Laplace and Cauchy distributions are also available.

Shift-scale models \bibcitepmlt::Siegfried_Kook_Hothorn_2023 of the form

P(Y \le y \mid X = x) = F_Z(\sqrt{\exp(s(x)^\top \gamma)} [(a(y) \otimes b(x))^\top \vartheta] + d(x)^\top \beta)

(scale_shift = FALSE) or

P(Y \le y \mid X = x) = F_Z(\sqrt{\exp(s(x)^\top \gamma)} [(a(y) \otimes b(x))^\top \vartheta + d(x)^\top \beta])

(scale_shift = TRUE) with bases a(y) (response), b(x) (interacting), d(x) (shifting), and s(x) (scaling) can be specified as well.