Decomposing main effects in moderated regression models

Previous research has used alternative moderated regression models (MRMs) (e.g., mean-centered MRM) to examine the interaction effect. The interaction effect remains fixed in alternative MRMs. In contrast, the main effects may change in alternative MRMs. Thus, it is common to examine moderation effects with the interaction effect only, although the main effects include useful information. This paper proposes a new MRM with which one can examine and interpret the main effects as well as the interaction effect meaningfully. The new MRM allows one to examine the effects of original predictors. Furthermore, it decomposes main effects into orthogonal components and correlated components. One may examine orthogonal components as the main effects separated from the interaction effect. In addition, one may examine correlated components to assess the degree to which the main effects are correlated with the interaction effect.