Lm {tram}

Normal Linear Model

Description

Normal linear model with benefits

Usage

Lm(formula, data, subset, weights, offset, cluster, na.action = na.omit, ...)

Arguments

formula

an object of class "formula": a symbolic description of the model structure to be fitted. The details of model specification are given under tram and in the package vignette.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula).

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 NULL or a numeric vector. If present, the weighted log-likelihood is maximised.

offset

this can be used to specify an _a priori_ known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases.

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 NAs. The default is set to na.omit.

...

additional arguments to tram.

Details

A normal linear model with simulaneous estimation of regression coefficients and scale parameter(s). This function also allows for stratum-specific intercepts and variances as well as censoring and truncation in the response.

Note that the scale of the parameters is different from what is reported by lm; the discrepancies are explained in the package vignette.

The model is defined with a negative shift term. Large values of the linear predictor correspond to large values of the conditional expectation response.

Value

An object of class Lm, with corresponding coef, vcov, logLik, estfun, summary, print, plot and predict methods.

References

Torsten Hothorn, Lisa Moest, Peter Buehlmann (2018), Most Likely Transformations, Scandinavian Journal of Statistics, 45(1), 110–134, doi:10.1111/sjos.12291.

Examples

  data("BostonHousing2", package = "mlbench")

  lm(cmedv ~ crim + zn + indus + chas + nox + rm + age + dis + 
             rad + tax + ptratio + b + lstat, data = BostonHousing2)

  Lm(cmedv ~ chas + crim + zn + indus + nox + 
             rm + age + dis + rad + tax + ptratio + b + lstat, 
             data = BostonHousing2)