Hierarchical Poisson Regression Modeling

Abstract

The Poisson model and analyses here feature nonexchangeable gamma distributions (although exchangeable following a scale transformation) for individual parameters, with standard deviations proportional to means. A relatively uninformative prior distribution for the shrinkage values eliminates the ill behavior of maximum likelihood estimators of the variance components. When tested in simulation studies, the resulting procedure provides better coverage probabilities and smaller risk than several other published rules, and thus works well from Bayesian and frequentist perspectives alike. The computations provide fast, accurate density approximations to individual parameters and to structural regression coefficients. The computer program is publicly available through Statlib.