Moment Testing for Interaction Terms in Structural Equation Modeling

Starting with Kenny and Judd (Psychol. Bull. 96:201–210, 1984) several methods have been introduced for analyzing models with interaction terms. In all these methods more information from the data than just means and covariances is required. In this paper we also use more than just first- and second-order moments; however, we are aiming to adding just a selection of the third-order moments. The key issue in this paper is to develop theoretical results that will allow practitioners to evaluate the strength of different third-order moments in assessing interaction terms of the model. To select the third-order moments, we propose to be guided by the power of the goodness-of-fit test of a model with no interactions, which varies with each selection of third-order moments. A theorem is presented that relates the power of the usual goodness-of-fit test of the model with the power of a moment test for the significance of third-order moments; the latter has the advantage that it can be computed without fitting a model. The main conclusion is that the selection of third-order moments can be based on the power of a moment test, thus assessing the relevance in the analysis of different sets of third-order moments can be computationally simple. The paper gives an illustration of the method and argues for the need of refraining from adding into the analysis an excess of higher-order moments.