Stratified Linear Transformation Models
Likelihood-inference for stratified linear transformation models
tram(formula, data, subset, weights, offset, cluster, na.action = na.omit,
distribution = c("Normal", "Logistic", "MinExtrVal", "MaxExtrVal", "Exponential"),
transformation = c("discrete", "linear", "logarithmic", "smooth"),
LRtest = TRUE, prob = c(0.1, 0.9), support = NULL,
bounds = NULL, add = c(0, 0), order = 6,
negative = TRUE, scale = TRUE, extrapolate = FALSE,
log_first = FALSE, sparse_nlevels = Inf,
model_only = FALSE, constraints = NULL, ...)
tram_data(formula, data, subset, weights, offset, cluster, na.action = na.omit)formula |
an object of class |
data |
an optional data frame, list or environment (or object
coercible by |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
weights |
an optional vector of weights to be used in the fitting
process. Should be |
offset |
this can be used to specify an _a priori_ known component to
be included in the linear predictor during fitting. This
should be |
cluster |
optional factor with a cluster ID employed for computing clustered covariances. |
na.action |
a function which indicates what should happen when the data
contain |
distribution |
character specifying how the transformation function is mapped into probabilities. Available choices include the cumulative distribution functions of the standard normal, the standard logistic and the standard minimum extreme value distribution. |
transformation |
character specifying the complexity of the response-transformation. For discrete responses, one parameter is assigned to each level (except the last one), for continuous responses linear, log-linear and smooth (parameterised as a Bernstein polynomial) function are implemented. |
LRtest |
logical specifying if a likelihood-ratio test for the null of all coefficients in the linear predictor being zero shall be performed. |
prob |
two probabilities giving quantiles of the response defining the support of a smooth
Bernstein polynomial (if |
support |
a vector of two elements; the support of a smooth
Bernstein polynomial (if |
bounds |
an interval defining the bounds of a real sample space. |
add |
add these values to the support before generating a grid via
|
order |
integer >= 1 defining the order of the Bernstein polynomial
(if |
negative |
logical defining the sign of the linear predictor. |
scale |
logical defining if variables in the linear predictor shall be scaled. Scaling is internally used for model estimation, rescaled coefficients are reported in model output. |
extrapolate |
logical defining the behaviour of the Bernstein transformation
function outside |
sparse_nlevels |
integer; use a sparse model matrix if the number
of levels of an ordered factor is at least as large as
|
log_first |
logical; if |
model_only |
logical, if |
constraints |
additional constraints on regression coefficients in
the linear predictor of the form |
... |
additional arguments. |
The model formula is of the form y | s ~ x where y is an at
least ordered response variable, s are the variables defining strata
and x defines the linear predictor. y ~ x defines a model
without strata (but response-varying intercept function) and y | s ~
0 sets-up response-varying coefficients for all variables in s.
The two functions tram and tram_data are not intended
to be called directly by users. Instead,
functions Coxph (Cox proportional hazards models),
Survreg (parametric survival models),
Polr (models for ordered categorical responses),
Lm (normal linear models),
BoxCox (non-normal linear models) or
Colr (continuous outcome logistic regression) allow
direct access to the corresponding models.
The model class and the specific models implemented in tram are explained in the package vignette of package tram. The underlying theory of most likely transformations is presented in Hothorn et al. (2018), computational and modelling aspects in more complex situations are discussed by Hothorn (2018).
An object of class tram inheriting from mlt.
Torsten Hothorn, Lisa Moest, Peter Buehlmann (2018), Most Likely Transformations, Scandinavian Journal of Statistics, 45(1), 110–134, doi: 10.1111/sjos.12291.
Torsten Hothorn (2018), Most Likely Transformations: The mlt Package, Journal of Statistical Software, forthcoming. URL: https://cran.r-project.org/package=mlt.docreg
data("BostonHousing2", package = "mlbench")
### unconstrained regression coefficients
### BoxCox calls tram internally
m1 <- BoxCox(cmedv ~ chas + crim + zn + indus + nox +
rm + age + dis + rad + tax + ptratio + b + lstat,
data = BostonHousing2)
### now with two constraints on regression coefficients
m2 <- BoxCox(cmedv ~ chas + crim + zn + indus + nox +
rm + age + dis + rad + tax + ptratio + b + lstat,
data = BostonHousing2,
constraints = c("crim >= 0", "chas1 + rm >= 1.5"))
coef(m1)
coef(m2)
K <- matrix(0, nrow = 2, ncol = length(coef(m2)))
colnames(K) <- names(coef(m2))
K[1, "crim"] <- 1
K[2, c("chas1", "rm")] <- 1
m3 <- BoxCox(cmedv ~ chas + crim + zn + indus + nox +
rm + age + dis + rad + tax + ptratio + b + lstat,
data = BostonHousing2,
constraints = list(K, c(0, 1.5)))
all.equal(coef(m2), coef(m3))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.