Overview: FMM Procedure

The FMM procedure fits statistical models to data for which the distribution of the response is a finite mixture of univariate distributions—that is, each response comes from one of several random univariate distributions with unknown probabilities. You can use PROC FMM to model the component distributions in addition to the mixing probabilities; see A Gentle Introduction to Finite Mixture Models for more precise definitions and discussion of similar but distinct modeling methodologies.

Classical statistical models are a special case of the finite mixture models in which the distribution of the data has only a single component.

Finite mixture models are useful for the following applications:

• estimating multimodal or heavy-tailed densities

• fitting zero-inflated or hurdle models to count data with excess zeros

• modeling overdispersed data

• fitting regression models with complex error distributions

• classifying observations based on predicted component probabilities

• accounting for unobservable, omitted variables

• estimating switching regressions

The FMM procedure is designed to fit finite mixtures of regression models or finite mixtures of generalized linear models in which the covariates and regression structure can be the same across components or might be different. You can fit finite mixture models by maximum likelihood or Bayesian methods.

For more information about the differences between the FMM procedure and other statistical modeling procedures in SAS/STAT software, see the section PROC FMM Contrasted with Other SAS Procedures.