Finite Mixture Models

TLDR: Finite mixture models as mentioned in this paper provide a natural way of modeling continuous or discrete outcomes that are observed from populations consisting of a finite number of homogeneous subpopulations, which are abundant in the social and behavioral sciences, biological and environmental sciences, engineering and finance.

Abstract: Finite mixture models provide a natural way of modeling continuous or discrete outcomes that are observed from populations consisting of a finite number of homogeneous subpopulations. Applications of finite mixture models are abundant in the social and behavioral sciences, biological and environmental sciences, engineering and finance. Such models have a natural representation of heterogeneity in a finite, usually small, number of latent classes, each of which may be regarded as a type. More generally, the finite mixture model can be shown to approximate any unknown distribution under suitable regularity conditions. The Stata package -fmm- implements a maximum likelihood estimator for a class of finite mixture models. In this talk, I will begin by introducing finite mixture models using a number of examples and discuss issues of estimation, testing and model selection. I will then describe estimation using fmm, calculations of predictions, marginal effects, and posterior class probabilities, and illustrate these using examples from econometrics and finance.