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SAS/STAT Topics

SAS/STAT Software

Finite Mixture Models

Finite mixture models provide a flexible framework for analyzing a variety of data. They are parametric models that enable you to describe an unknown distribution in terms of mixtures of known distributions. They enable you to assess the probabilities of events or simulate draws from the unknown distribution the same way you do when your data are from a known distribution.

The SAS/STAT finite mixture models procedures include the following:

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. The following are highlights of the FMM procedure's features:

  • model the component distributions in addition to the mixing probabilities
  • fit finite mixture models by maximum likelihood or Bayesian methods
  • fit finite mixtures of regression and generalized linear models
  • define the model effects for the mixing probabilities and their link function
  • model overdispersed data
  • estimate multimodal or heavy-tailed densities
  • fit zero-inflated or hurdle models to count data with excess zeros
  • fit regression models with complex error distributions
  • classify observations based on predicted component probabilities
  • twenty five different response distributions
  • linear equality and inequality constraints on model parameters
  • specify the response variable by using either the response syntax or the events/trials syntax
  • automated model selection for homogeneous mixtures
  • weighted estimation
  • control the performance characteristics of the procedure (for example, the number of CPUs, the number of threads for multithreading, and so on)
  • obtain separate analyses on observations in groups
  • create a data set that contains observationwise statistics that are computed after fitting the model
  • create a SAS data set corresponding to any output table
  • automatically create graphs by using ODS Graphics
For further details, see FMM Procedure