Structural Equation Modeling: Mixture Models

Abstract This article discusses a modeling framework that links two well‐known statistical methods: structural equation modeling (SEM) and latent class or finite mixture modeling. Mixture SEM can either be viewed as a refinement of multivariate normal (MVN) mixtures, where the within‐class covariance matrices are smoothed according to a postulated SEM structure, or as a form of multiple group SEM, in which the group variable is unobserved. After introducing standard MVN mixtures, it is shown how the SEM framework can be used to restrict the class‐specific means and covariances. Furthermore, parameter estimation, model testing, and software is discussed, and an empirical example is provided.