More on Transformations and Moderated Regression Analysis: Advantages of Additivity and Homoscedasticity Transformations

Abstract

This article addresses advantages of performing transformations that eliminate interactions in both moderated regression and analysis of variance models, when these transformations also result in homoscedasticity, and when the transformed scores attain at least the same level of measurement as the raw scores. It is shown that these transformations are in fact what have been called subgroup variance equating transformations (SVET), though equality of subgroup variances is a side effect of eliminating interactions and heteroscedasticity. Moderated regression analyses of these transformed data have the following advantages over comparable analyses of raw data: (a) greater tenability of the assumptions of analysis of variance (and moderated regression) models, (b) potentially much greater sensitivity of main effects significance tests, and (c) simpler (more parsimonious) interpretations.