Structural Equation Modeling, 2nd Edition

6 Mixture modeling

6.1 Introduction

Like the traditional analytical approaches, such as analysis of variance (ANOVA), multiple regression, and mixed (i.e. multilevel) models, the models discussed in previous chapters of this book are all variable‐centered analytical approaches that focus on relations among variables and assume the sample under study arises from a homogeneous population. In recent years, mixture models (or finite mixture models) have increasingly gained in popularity as a framework for person‐centered analytic approaches (Clogg 1995; Collins and Lanza 2010; Everitt 1980; Heinen 1993; Muthén 2001, 2002; Nagin 1999, 2005; Vermunt and Magidson 2002). Unlike the variable‐centered approaches, the person‐centered analytical approaches focus on identifying unobserved subpopulations comprising similar individuals, and involve modeling a mixture outcome distribution (most often a mixture of unobserved normal or Gaussian distributions). The mixture of different distributions indicates population heterogeneity; in other words, the sample observations arise from a finite number of unobserved subpopulations in the target population.1 For example, the earliest account of a mixture model is attributed to a study of the asymmetric frequency distribution of measurements of the frontal breadth of shore crabs. The asymmetric frequency distribution arose from the fact that the units grouped together in the measured material were not homogenous, but a two‐component Gaussian ...