RAND Statistics Seminar Series

Random Effects Models for Dyadic Network Data

Presented by Peter Hoff, Assistant Professor
Departments of Statistics and Biostatistics
Center for Statistics and the Social Sciences
University of Washington
Thursday, May 15, 2003 4:00 pm
Main Conference Room

Abstract

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.