RAND Statistics Seminar Series

Identification of the Variance Components in the
General Two-Variance Linear Model

Presented by Jim Hodges
Senior Research Associate, Division of Biostatistics and Director, Biostatistics Core
Minnesota Oral Health Clinical Research Center
University of Minnesota
Friday, February 11, 2005, 10:30 a.m.
Forum m-1224, Santa Monica


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 talk, we introduce the class of two-variance hierarchical linear models and characterize the aspects of these models that led to well-identified or poorly identified variances. These ideas are illustrated with a spatial analysis of a periodontal dataset and examined in some generality for a specific two-variance model, the conditional autoregressive (CAR) model. 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.