COVARIATE SELECTION IN HIERARCHICAL MODELS OF HOSPITAL ADMISSION COUNTS: A BAYES FACTOR APPROACH

The Bayes factor is employed to select covariates for a hierarchical model applied to a collection of hospital admission counts. Integrals representing the Bayes factor numerator and denominator marginal probabilities are intractable for the model used. We examine three approaches to integral approximation: Laplace approximation, Monte Carlo integration, and a Markov chain Monte Carlo (MCMC) approach. Laplace-approximated Bayes factors are found to be nearly unbiased, and can be obtained very quickly. MCMC was used to implement an importance sampling scheme. The resulting approximate Bayes factors exhibited some bias and were obtained at a relatively high cost in computer time. Software to implement the Laplace approximation is available from StatLib.