On the Merits of Orthogonalizing Powered and Product Terms: Implications for Modeling Interactions Among Latent Variables

TLDR: In this paper, the authors highlight the merits of residual centering for representing interaction and powered terms in standard regression contexts (e.g., Lance, 1988), and propose an orthogonalizing approach to represent latent variable interactions.

Abstract: The goals of this article are twofold: (a) briefly highlight the merits of residual centering for representing interaction and powered terms in standard regression contexts (e.g., Lance, 1988), and (b) extend the residual centering procedure to represent latent variable interactions. The proposed method for representing latent variable interactions has potential advantages over extant procedures. First, the latent variable interaction is derived from the observed covariation pattern among all possible indicators of the interaction. Second, no constraints on particular estimated parameters need to be placed. Third, no recalculations of parameters are required. Fourth, model estimates are stable and interpretable. In our view, the orthogonalizing approach is technically and conceptually straightforward, can be estimated using any structural equation modeling software package, and has direct practical interpretation of parameter estimates. Its behavior in terms of model fit and estimated standard errors is v...