A Comparison of Poisson, Negative Binomial, and Semiparametric Mixed Poisson Regression Models

Kenneth C. Land, L. McCALL Patricia and Daniel S. Nagin
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Kenneth C. Land: Duke University
L. McCALL Patricia: North Carolina State University
Daniel S. Nagin: Carnegie-Mellon University

Sociological Methods & Research, 1996, vol. 24, issue 4, 387-442

Abstract: Specifications and moment properties of the univariate Poisson and negative binomial distributions are briefly reviewed and illustrated. Properties and limitations of the corresponding poisson and negative binomial (gamma mixtures of Poissons) regression models are described. It is shown how a misspecification of the mixing distribution of a mixed Poisson model to accommodate hidden heterogeneity ascribable to unobserved variables—although not affecting the consistency of maximum likelihood estimators of the Poisson mean rate parameter or its regression parameterization—can lead to inflated t ratios of regression coefficients and associated incorrect inferences. Then the recently developed semiparametric maximum likelihood estimator for regression models composed of arbitrary mixtures of Poisson processes is specified and further developed. It is concluded that the semiparametric mixed Poisson regression model adds considerable flexibility to Poisson-family regression models and provides opportunities for interpretation of empirical patterns not available in the conventional approaches.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:sae:somere:v:24:y:1996:i:4:p:387-442

DOI: 10.1177/0049124196024004001

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