Decomposing Main Effects in Moderated Regression Models

A moderated regression model ( MRM ) suffers from the correlations of the interaction effect with the main effects. The interaction effect is invariant, but the main effects are not invariant in the MRM and its transformed models. Thus, it is common to examine only the interaction effect. This paper shows that the main effects can be represented as sums of two components in the MRM : orthogonal components and correlated components. The orthogonal components are independent from the interaction effect and they are invariant like the interaction effect. Thus, it is possible to interpret the orthogonal components like the main effects in ANOVA . In contrast, the correlated components capture the effects resulting from the correlations of the interaction effect with the main effects. Furthermore, this paper shows that it is possible to decompose simple slopes and cross-over values with the two components of main effects