Empirical Bayes estimation for logistic regression and extended parametric regression models

Parametric empirical Bayes methods are discussed for estimating the mean proportion response from generalized linear regression models (GLiM's) based on the binomial distribution, including the well-known case of logistic regression. The GLiM's are extended via parametric families of link functions that embed specific links - such as the logit - within their parametric structure. The models may be viewed as members of a larger class of conditionally independent hierarchical models. An example from environmental mutagenesis, wherein a hierarchical effect is induced by similarities among responding units, motivates consideration of the hierarchical GLiM. Empirical Bayes estimation of the mean proportion response is addressed for this example, with emphasis directed at extensions of the logit model.