Estimating and interpreting latent variable interactions A tutorial for applying the latent moderated structural equations method

• Published in: International journal of behavioral development Vol. 39; no. 1; pp. 87 - 96
• Main Authors: Maslowsky, Julie, Jager, Justin, Hemken, Douglas
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.01.2015
• Subjects: Computation; Effect Size; Goodness of Fit; Interaction; Monte Carlo Methods; Multivariate Analysis; Statistical Analysis; Structural Equation Models; latent variables; structural equation modeling; methodology
• ISSN: 0165-0254; 1464-0651
• DOI: 10.1177/0165025414552301

Latent variables are common in psychological research. Research questions involving the interaction of two variables are likewise quite common. Methods for estimating and interpreting interactions between latent variables within a structural equation modeling framework have recently become available. The latent moderated structural equations (LMS) method is one that is built into Mplus software. The potential utility of this method is limited by the fact that the models do not produce traditional model fit indices, standardized coefficients, or effect sizes for the latent interaction, which renders model fitting and interpretation of the latent variable interaction difficult. This article compiles state-of-the-science techniques for assessing LMS model fit, obtaining standardized coefficients, and determining the size of the latent interaction effect in order to create a tutorial for new users of LMS models. The recommended sequence of model estimation and interpretation is demonstrated via a substantive example and a Monte Carlo simulation. Finally, extensions of this method are discussed, such as estimating quadratic effects of latent factors and interactions between latent slope and intercept factors, which hold significant potential for testing and advancing developmental theories.