We consider an extension of the generalized linear model by introducing conjugate priors for the canonical parameters. The hyperparameter is assumed to follow a noninformative hyper-prior distribution p. When p is known, the regression parameter b is estimated by maximizing the unconditional marginal likelihood function for b. When p is not known, we propose an empirical Bayes approach to estimate p via an EM algorithm. The ideas are illustrated using a data set concerning urinary tract infections among college women.