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A comparison of Poisson, negative binomial, and semiparametric mixed Poisson regression models: With empirical applications to criminal careers data

Publication ,  Journal Article
Land, KC; McCall, PL; Nagin, DS
Published in: Sociological Methods and Research
January 1, 1996

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

Published In

Sociological Methods and Research

DOI

ISSN

0049-1241

Publication Date

January 1, 1996

Volume

24

Issue

4

Start / End Page

387 / 442

Related Subject Headings

  • Social Sciences Methods
  • 4905 Statistics
  • 4410 Sociology
  • 1608 Sociology
  • 1117 Public Health and Health Services
  • 0104 Statistics
 

Citation

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Land, K. C., McCall, P. L., & Nagin, D. S. (1996). A comparison of Poisson, negative binomial, and semiparametric mixed Poisson regression models: With empirical applications to criminal careers data. Sociological Methods and Research, 24(4), 387–442. https://doi.org/10.1177/0049124196024004001
Land, K. C., P. L. McCall, and D. S. Nagin. “A comparison of Poisson, negative binomial, and semiparametric mixed Poisson regression models: With empirical applications to criminal careers data.” Sociological Methods and Research 24, no. 4 (January 1, 1996): 387–442. https://doi.org/10.1177/0049124196024004001.
Land, K. C., et al. “A comparison of Poisson, negative binomial, and semiparametric mixed Poisson regression models: With empirical applications to criminal careers data.” Sociological Methods and Research, vol. 24, no. 4, Jan. 1996, pp. 387–442. Scopus, doi:10.1177/0049124196024004001.
Journal cover image

Published In

Sociological Methods and Research

DOI

ISSN

0049-1241

Publication Date

January 1, 1996

Volume

24

Issue

4

Start / End Page

387 / 442

Related Subject Headings

  • Social Sciences Methods
  • 4905 Statistics
  • 4410 Sociology
  • 1608 Sociology
  • 1117 Public Health and Health Services
  • 0104 Statistics