Bridging Conditional and Marginal Inference for Spatially Referenced Binary Data

• Activity Number: 597
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Laura Boehm*+ and Brian Reich and Dipankar Bandyopadhyay
• Companies: North Carolina State University and North Carolina State University and
• Keywords: bridge density ; copula ; logistic link ; marginal inference ; random effects

Abstract

Spatially-referenced binary data are common in epidemiology and public health. Owing to its elegant log-odds interpretation of the regression coefficients, a natural model for these data is logistic regression. In the case of spatially correlated binary response, typical modeling choices are Gaussian random effects models, in which coefficients must be interpreted conditionally, or a range of marginally specified models, each with its own drawbacks. Here we propose a new spatial random effects distribution through a copula framework which ensures that the regression coefficients maintain the log-odds interpretation both conditional on and marginally over the spatial random effects. We present simulations to assess the robustness of our proposition to various random effects, and apply it to an interesting dataset assessing periodontal health of Gullah-speaking African Americans. The proposed methodology is flexible enough to handle areal or geo-statistical datasets and hierarchical models with multiple random intercepts.