Orthogonalizing Through Residual Centering

Abstract

Residual centering is a useful tool for orthogonalizing variables and latent constructs, yet it is underused in the literature. The purpose of this article is to encourage residual centering’s use by highlighting instances where it can be helpful: modeling higher order latent variable interactions, removing collinearity from latent constructs, creating phantom indicators for multiple group models, and controlling for covariates prior to latent variable analysis. Residual centering is not without its limitations, however, and the authors also discuss caveats to be mindful of when implementing this technique. They discuss the perils of double orthogonalization (i.e., simultaneously orthogonalizing A relative to B and B relative to the original A), the unintended consequences of orthogonalization on model fit, the removal of a mean structure, and the effects of nonnormal data on residual centering.