Specification of conditional transformation models
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")), ...)An object of class ctm.
a basis function, ie, an object of class basis
a basis function, ie, an object of class basis
a basis function, ie, an object of class basis
a basis function, ie, an object of class basis
a logical choosing between two different model types
in the presence of a scaling term
either a data.frame containing the model variables
or a formal description of these variables in an object of class vars
a character vector describing the distribution to be transformed
a logical indicating if sum constraints shall be applied
arguments to as.basis when shifting is a formula
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.
Torsten Hothorn, Lisa Moest, Peter Buehlmann (2018), Most Likely Transformations, Scandinavian Journal of Statistics, 45(1), 110--134, 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, tools:::Rd_expr_doi("10.1080/00031305.2023.2203177").