Prediction Techniques for Box-Cox Regression Models

This article reviews several techniques useful for forming point and interval predictions in regression models with Box-Cox transformed variables. The techniques reviewed--plug-in, mean squared error analysis, predictive likelihood, and stochastic simulation--take account of nonnormality and parameter uncertainty in varying degrees. A Monte Carlo study examining their small-sample accuracy indicates that uncertainty about the Box-Cox transformation parameter may be relatively unimportant. For certain parameters, deterministic point predictions are biased and plug-in prediction intervals are also biased. Stochastic simulation, as usually carried out, leads to badly biased predictions. A modification of the usual approach renders stochastic simulation predictions largely unbiased.