Specification, Estimation, and Testing of Moment Structure Models Based on Latent Variates Involving Interactions among the Exogenous Constructs

This article shows how methods for the analysis of moment structures based on latent variates can be used to investigate theories hypothesizing interactive effects of exogenous constructs on endogenous constructs. Building on the work of Kenny and Judd, the authors discuss the specification of structural equation models with latent interaction terms, and they show that the structural coefficient relating an endogenous construct to the interaction of two exogenous constructs does not depend on the origin of the components of the multiplicative exogenous construct. The authors report evidence from simulations that the 2 statistics and standard errors provided by maximum likelihood and generalized least squares may not be trustworthy, but that model testing through robust and asymptotically distribution-free procedures leads to appropriate assessments of model fit and the significance of parameter estimates. They conclude the article with an application of the procedure to the context of expectancy-value attitude models.