A comparison of Poisson, negative binomial, and semiparametric mixed Poisson regression models: With empirical applications to criminal careers data
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.
Duke Scholars
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Related Subject Headings
- Social Sciences Methods
- 4905 Statistics
- 4410 Sociology
- 1608 Sociology
- 1117 Public Health and Health Services
- 0104 Statistics
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Social Sciences Methods
- 4905 Statistics
- 4410 Sociology
- 1608 Sociology
- 1117 Public Health and Health Services
- 0104 Statistics