Structural Equation Models of Latent Interactions: Clarification of Orthogonalizing and Double-Mean-Centering Strategies

The purpose of this investigation is to compare a new (double-mean-centering) strategy to estimating latent interactions in structural equation models with the (single) mean-centering strategy (Marsh, Wen, Hau, 2004, 2006) and the orthogonalizing strategy (Little, Bovaird, Widaman, 2006; Marsh et al., 2007). A key benefit of the orthogonalizing strategy is that it eliminated the need to estimate a mean structure as required by the mean-centering strategy, but required a potentially cumbersome 2-step estimation procedure. In contrast, the double-mean-centering strategy eliminates both the need for the mean structure and the cumbersome 2-stage estimation procedure. Furthermore, although the orthogonalizing and double-mean-centering strategies are equivalent when all indicators are normally distributed, the double-mean-centering strategy is superior when this normality assumption is violated. In summary, we recommend that applied researchers wanting to estimate latent interaction effects use the double-mean-centering strategy instead of either the single-mean-centering or orthogonalizing strategies, thus allowing them to ignore the cumbersome mean structure.