STEMM: A General Finite Mixture Structural Equation Model

Abstract

This paper provides a general Structural Equation finite Mixture Model and algorithm (STEMM). Substantively, the model allows the researcher to simul­taneously treat heterogeneity and form groups in the context of a postulated causal (i.e., simultaneous equation regression) structure in which all the observables are measured with error. Methodologically, the model is more general than such sta­tistical methods as cluster analysis, confirmatory multigroup factor analysis, and multigroup structural equation models. In particular the general finite mixture model includes, as special cases, finite mixtures of simultaneous equations with feedback, confirmatory factor analysis, and confirmatory second-order factor models. We describe the statistical theory, present simulation evidence on the per­formance of the EM estimation algorithm, and apply the model to a psychological study on the role of emotion in goal-directed behavior. Finally we discuss several avenues for future research.

Keywords: Structural equations, Finite mixtures, Maximum likelihood, Emo­tions, Weight loss