Empirical Bayes analysis for a hierarchical poisson generalized linear model

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7 Scopus citations

Abstract

We describe a hierarchical Poisson regression model for count data with possible extra-Poisson variation. This model depicts the effects of explanatory variables through a generalized linear model embedded at the prior level of the hierarchy. Model parameters are estimated in a parametric empirical Bayes framework under various estimation schemes. Properties of consistency and asymptotic normality for the hyperparameter estimators are established under the assumption that the number of observations at each treatment (or treatment combination) are large while the number of treatment levels remains fixed. These asymptotic properties form the basis for the large sample inferences on the hyperparameters. An example illustrates use of the methodology in practice.

Original languageEnglish (US)
Pages (from-to)235-248
Number of pages14
JournalJournal of Statistical Planning and Inference
Volume111
Issue number1-2
DOIs
StatePublished - Feb 1 2003
Externally publishedYes

Keywords

  • Asymptotic theory
  • Count data
  • Extra-poisson variability
  • Hierarchical model
  • Maximum likelihood
  • Parametric empirical Bayes analysis
  • Quasi-likelihood

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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