Generalized linear models with random effects; Salamander mating revisited

In recent years much effort has been devoted to extending regression methodology to non-Gaussian data, where responses are not independent. These methods for dependent responses are suitable for data from longitudinal studies or nested designs. However, use of these methods for crossed designs seems to have serious limitations due to the intensive computations involved because of the intractable nature of the joint distribution. In this paper, we cast the problem in a Bayesian framework and use a Monte Carlo method, the Gibbs sampler, to avoid current computational limitations. The flexibility of this approach is illustrated by analyzing the interesting salamander mating data reported by McCullagh and Nelder (1989, Generalized Linear Models, 2nd edition, London: Chapman and Hall).