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Bayesian Inference for Finite Mixtures of Generalized Linear Models with Random Effects

Published online by Cambridge University Press:  02 January 2025

Peter J. Lenk  and
Wayne S. DeSarbo
Peter J. Lenk*
Affiliation:
The University of Michigan Business School
Wayne S. DeSarbo
Affiliation:
Pennsylvania State University
*
Requests for reprints should be sent to Peter J. Lenk, University of Michigan Business School, 701 Tappan Street, Ann Arbor MI 48109-1234.
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Abstract

We present an hierarchical Bayes approach to modeling parameter heterogeneity in generalized linear models. The model assumes that there are relevant subpopulations and that within each subpopulation the individual-level regression coefficients have a multivariate normal distribution. However, class membership is not known a priori, so the heterogeneity in the regression coefficients becomes a finite mixture of normal distributions. This approach combines the flexibility of semiparametric, latent class models that assume common parameters for each sub-population and the parsimony of random effects models that assume normal distributions for the regression parameters. The number of subpopulations is selected to maximize the posterior probability of the model being true. Simulations are presented which document the performance of the methodology for synthetic data with known heterogeneity and number of sub-populations. An application is presented concerning preferences for various aspects of personal computers.

Keywords

Bayesian inferenceconsumer behaviorfinite mixturesgeneralized linear modelsheterogeneitylatent class analysisMarkov chain Monte Carlo
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 1 , March 2000 , pp. 93 - 119
Copyright
Copyright © 2000 The Psychometric Society

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