Detecting Interaction Using a Two-way Multigroup Common Factor Model

In this paper, a two-way multigroup common factor model (MG-CFM) is presented, which can be used to estimate two-way interaction between grouping variables on latent variables. By applying a likelihood ratio test, a two-way interaction can be tested. The effectiveness of this MG-CFM likelihood ratio test is evaluated in a Monte Carlo simulation, comparing statistical power and robustness to MANOVA’s F-test. The results of the simulation show that Type-I error control is satisfactory for both tests and considerable higher power can be achieved when a MG-CFM is used rather than a MANOVA