Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 3, 548--565

Modelling Count Data by Random Effect Poisson Model

By

Pushpa L. Gupta and Ramesh C. Gupta, University of Maine, Orono, USA
S.H. Ong, University of Malaya, Malaysia

SUMMARY. It is well known that count data show overdispersion compared to the Poisson distribution, which is extensively used for the analysis of discrete data. In order to account for the unobserved heterogeneity, in this paper we introduce  an additive and a multiplicative random effect Poisson model. The random effect is modelled by the gamma distribution and the inverse Gaussian distribution and both univariate as well as multivariate models are developed. Expressions for the various conditionals and marginal distributions are obtained and the correlation introduced by sharing a common random effect is studied. Some computational aspects, of the models developed , are presented to illustrate the results. Thus the purpose of this paper is to provide some alternative models that can be used for analysing data which shows overdispersion.

AMS (1991) subject classification}. Primary 62F03; secondary 62E10, 62H05.

Key words and phrases. Overdispersion, additive random effect, multiplicative random effect, gamma distribution, inverse Gaussian distribution.

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