A Method of Moments Technique for Fitting Interaction Effects in Structural Equation Models

The desire to fit structural equation models containing an interaction term has received much methodological attention in the social science literature. This paper presents a technique for the cross-product structural model that utilizes factor score estimates and results in closed-form moments-type estimators. The technique, which does not require normality for the underlying factors, was originally introduced in a very general form by Wall and Amemiya (2000) for any polynomial structural model. In this paper, the practical implementation of this method, including standard error estimation, is presented specifically for the cross-product model. The procedure is applied to an example from social/behavioural epidemiology where the flexibility of the cross-product model provides a useful description of the underlying theory. A simulation study is also presented comparing the method of moments for the cross-product model with three other procedures.