Mixture Models

Mixture models were created to decompose nonnormal univariate or multivariate distributions into distinct (i.e., a mixture of) normal distributions. In the social sciences, mixture models are typically referred to as person-centered analyses and used to identify distinct subpopulations of participants, referred to as profiles, differing from one another quantitatively and qualitatively on a series of indicators and/or relations among indicators. Quantitative research typically relies on statistics (e.g., correlations, regressions) obtained from a sample to infer what happens in the population from which the sample was extracted. Mixture models relax this assumption of population homogeneity (i.e., that [Page 933]the results can be generalized to all members of the population) to extract subpopulations (i.e., profiles) characterized by a distinct set of results. After briefly reviewing the history ...