Estimation of a common slope in a gamma regression model with multiple strata: An empirical Bayes method

An empirical Bayes method for a gamma regression model with a slope parameter [beta] common through multiple strata is proposed and examined. Assuming that the number of strata is fairly large, we attempt to modify a usual empirical Bayes method so as to yield an improved estimator of [beta]. Such a modification is necessary to pursue compromise between Bayesian and frequentist approaches. Simulation studies strongly support superiority of the proposed estimator over the maximum likelihood estimator. A test for [beta]=0 is also discussed. To show large difference between the two estimates, an illustrative example is given.