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Journal of Classification

, Volume 12, Issue 1, pp 21–55 | Cite as

A mixture likelihood approach for generalized linear models

  • Michel Wedel
  • Wayne S. DeSarbo
Article

Abstract

A mixture model approach is developed that simultaneously estimates the posterior membership probabilities of observations to a number of unobservable groups or latent classes, and the parameters of a generalized linear model which relates the observations, distributed according to some member of the exponential family, to a set of specified covariates within each Class. We demonstrate how this approach handles many of the existing latent class regression procedures as special cases, as well as a host of other parametric specifications in the exponential family heretofore not mentioned in the latent class literature. As such we generalize the McCullagh and Nelder approach to a latent class framework. The parameters are estimated using maximum likelihood, and an EM algorithm for estimation is provided. A Monte Carlo study of the performance of the algorithm for several distributions is provided, and the model is illustrated in two empirical applications.

Key Words

Mixture models Generalized linear models EM algorithm Maximum likelihood estimation 

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  1. 1.Department of Business Administration and Management Science, Faculty of EconomicsUniversity of GroningenGroningenThe Netherlands
  2. 2.University of MichiganUSA

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