Lehmann {tram}

Proportional Reverse Time Hazards Linear Regression

Description

Non-normal linear regression for Lehmann-alternatives

Usage

Lehmann(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

This transformation model uses the cumulative distribution function for the standard Gumbel maximum extreme value distribution to map the shifted transformation function into probabilities. The exponential of the shift paramater can be interpreted as a Lehmann-alternative or reverse time hazard ratio.

Value

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

References

Erich L. Lehmann (1953), The Power of Rank Tests, The Annals of Mathematical Statistics, 24(1), 23-43.

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)

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