ctm: Conditional Transformation Models

In mlt: Most Likely Transformations

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")), ...)

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
...	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). Hothorn et al. (2018) 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 (Siegfried et al., 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.

Value

An object of class ctm.

References

Torsten Hothorn, Lisa Moest, Peter Buehlmann (2018), Most Likely Transformations, Scandinavian Journal of Statistics, 45(1), 110–134, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/sjos.12291")}.

Sandra Siegfried, Lucas Kook, Torsten Hothorn (2023), Distribution-Free Location-Scale Regression, The American Statistician, 77(4), 345–356, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00031305.2023.2203177")}.

mlt documentation built on April 11, 2025, 3:09 p.m.