HIERARCHICAL POISSON REGRESSION MODELING

The Poisson model and analyses here feature nonexchangeable gamma dist ributions (although exchangeable following a scale trans formation) fo r individual parameters, with standard deviations proportional to mean s. A relatively uninformative prior distribution for the shrinkage val ues eliminates the ill behavior of maximum likelihood estimators of th e variance components, When rested in simulation studies, the resultin g procedure provides better coverage probabilities and smaller risk th an several other published rules, and thus works well from Bayesian an d frequentist perspectives alike. The computations provide fast, accur ate density approximations to individual parameters and to structural regression coefficients. The computer program is publicly available th rough Statlib.