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

Abstract

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 Marsh, H. W., Wen, Z. and Hau, K. T. 2004. Structural equation models of latent interactions: Evaluation of alternative estimation strategies and indicator construction.. Psychological Methods, 9: 275–300. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar], 2006 Marsh, H. W., Wen, Z. and Hau, K. T. 2006. “Structural equation models of latent interaction and quadratic effects”. In A second course in structural equation modeling Edited by: Hancock, G. and Mueller, R. 225–265. Greenwich, CT: Information Age. [Google Scholar]) and the orthogonalizing strategy (Little, Bovaird, & Widaman, 2006 Little, T. D., Bovaird, J. A. and Widaman, K. F. 2006. On the merits of orthogonalizing powered and product term: Implications for modeling interactions among latent variables.. Structural Equation Modeling, 13: 497–519. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Marsh et al., 2007 Marsh, H. W., Wen, Z., Hau, K. T., Little, T. D., Bovaird, J. A. and Widaman, K. F. 2007. Unconstrained structural equation models of latent interactions: Contrasting residual- and mean-centered approaches.. Structural Equation Modeling, 14: 570–580. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). 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.