Testing for two-way interactions in the multi-group common factor model

Abstract

In this article, a 2-way multigroup common factor model (MG-CFM) is presented. The MG-CFM can be used to estimate interaction effects between 2 grouping variables on 1 or more hypothesized latent variables. For testing the significance of such interactions, a likelihood ratio test is presented. In a simulation study, the robustness of the likelihood ratio test under different sample size conditions is studied and the likelihood ratio test is compared to the Wilks's lambda F test in multivariate analysis of variance (MANOVA) with respect to the approximated power to detect a 2-way interaction effect on a single latent variable. The manipulated factors are the number of indicators, the values of factor loadings, the sample size, and the interaction effect size. The results of the simulation study show that the Type I error rate of the likelihood ratio test is satisfactory and that under all conditions, the approximated power of the likelihood ratio test is considerably higher than that of the Wilks's lambda F test in MANOVA.