Chapter 6
Mixture Modeling
Like the traditional analytical approaches, such as ANOVA, multiple regression and mixed (i.e., multilevel) models, the models discussed in previous chapters of this book are all variable-centered 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 a person-centered analytic approach (Everitt, 1980; Heinen, 1993; Clogg, 1995; Nagin, 1999, 2005; Muthén, 2001, 2002; Vermunt and Magidson, 2002; Collins and Lanza, 2010). Different from the variable-centered approaches, the person-centered approaches focus on identifying unobserved subpopulations comprised of similar individuals or cases, 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 mixture density, indicating that the ...
