FRIDAY, February 18, 2005
Time: 1:30 - 2:30 PM
Constant 1047

Brian Reich
Department of Biostatistics
University of Minnesota

Bayesians frequently employ two-stage hierarchical models consisting of two variance parameters: one controlling measurement error and the other controlling the degree of smoothing implied by the model's higher level. These analyses can be hampered by poorly-identified variances which may lead to difficulty in computing and in choosing reference priors for these parameters. In this paper, we introduce the class of two-variance hierarchical linear models and characterize the aspects of these models that lead to well-identified or poorly-identified variances. These ideas are illustrated with a spatial analysis of a periodontal data set and examined in some generality for specific two-variance models including the conditionally autoregressive (CAR), one-way random effects, and multiple membership models. We also connect this theory with other constrained regression methods and suggest a diagnostic that can be used to search for missing spatially-varying fixed effects in the CAR model.