Maximum likelihood estimation of latent interaction effects with the LMS method

In the context of structural equation modeling, a general interaction model with multiple latent interaction effects is introduced. A stochastic analysis represents the nonnormal distribution of the joint indicator vector as a finite mixture of normal distributions. The Latent Moderated Structural Equations (LMS) approach is a new method developed for the analysis of the general interaction model that utilizes the mixture distribution and provides a ML estimation of model parameters by adapting the EM algorithm. The finite sample properties and the robustness of LMS are discussed. Finally, the applicability of the new method is illustrated by an empirical example. This research has been supported by a grant from the Deutsche Forschungsgemeinschaft, Germany, No. Mo 474/1 and Mo 474/2. The data for the empirical example have been provided by Andreas Thiele of the University of Frankfurt, Germany. The authors are indebted to an associate editor and to three anonymous reviewers ofPsychometrika whose comments and suggestions have been very helpful.