January, 2007
In analyzing data from multiple related studies, it is often of interest to borrow information across studies and to cluster similar studies. Although parametric hierarchical models are commonly used, a concern is sensitivity to the form chosen for the random effects distribution. A Dirichlet process (DP) prior can allow the distribution to be unknown, while clustering studies. However, the DP does not allow local clustering of studies with respect to a subset of the coefficients without making independence assumptions. Motivated by this problem, we propose a matrix stick-breaking process (MSBP) as a prior for a matrix of random probability measures. Theoretical properties of the MSBP are considered in detail, and methods are developed for posterior computation using MCMC. Using the MSBP as a prior for a matrix of study-specific regression coefficients, we demonstrate advantages over parametric modeling in simulated examples. The methods are further illustrated using a multinational uterotrophic bioassay study.
Keywords: Clustering; Dirichlet process; Hierarchical model; Mixture model; Nonparametric Bayes; Random effects.
The manuscript is available in PDF formats.