BoxCox {tram}

(Similar to) Box-Cox Models

Description

Non-normal linear regression inspired by Box-Cox models

Usage

BoxCox(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 model for transformed responses, where the transformation is estimated from the data simultaneously with the regression coefficients. This is similar to a Box-Cox transformation, but the technical details differ. Examples can be found 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 (but this relationship is potentially nonlinear).

Value

An object of class BoxCox, 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)

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