ctm {mlt} | 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")), ...)
Arguments
response |
a basis function, ie, an object of class |
interacting |
a basis function, ie, an object of class |
shifting |
a basis function, ie, an object of class |
scaling |
a basis function, ie, an object of class |
scale_shift |
a logical choosing between two different model types
in the presence of a |
data |
either a |
todistr |
a character vector describing the distribution to be transformed |
sumconstr |
a logical indicating if sum constraints shall be applied |
... |
arguments to |
Details
Specification of a transformation model 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
). All except
response
can be missing (in this case an unconditional distribution
is estimated).
This function only specifies the model which can then be fitted using
mlt
. The shift term is positive by default.
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.
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, doi:10.1111/sjos.12291.