Box and Cox power-transformation to additivity and homoscedasticity in regression

Abstract

We describe a Box and Cox power-transformation to simultaneously provide additivity and homoscedasticity in regression. The two methods developed here are extensions of the power-additive transformation (PAT) discussed by Goto (1992, 1995) and Hamasaki and Goto (2005). The PAT aims to improve the additivity or linearity of some simple model represented by linear predicators. We then consider combinations of the PAT with the weighting and transform-both-sides methods. We discuss the procedures to find the maximum likelihood estimates of parameters and then consider the relationship between the methods. Also, we compare the performances of the methods through a simulation study.