A Multivariate Spatial Mixture Model for Areal Data: Examining Regional Differences in Standardized Test Scores

• Activity Number: 266
• Type: Invited
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Brian Neelon*+ and Alan Gelfand
• Companies: Duke University and Duke University
• Keywords: Areal data ; Bayesian analysis ; Conditional autoregressive (CAR) prior ; Education data ; Mixture model ; Multivariate spatial data analysis

Abstract

Motivated by a study exploring geographic disparities in test scores among fourth graders in North Carolina, we develop a multivariate mixture model for the spatial analysis of correlated continuous outcomes. The responses are modeled as a finite mixture of multivariate normals, which accommodates a wide range of marginal response distributions and allows investigators to examine covariate effects within subpopulations of interest. The model has a hierarchical structure incorporating both individual- and areal-level predictors as well as spatial random effects for each mixture component. Conditional autoregressive priors on the random effects provide spatial smoothing and allow the shape of the multivariate distribution to vary flexibly across geographic regions. By integrating over this distribution, we obtain region-specific joint, marginal, and conditional inferences of interest. We adopt a Bayesian modeling approach and develop an efficient posterior sampling algorithm that relies primarily on closed-form full conditionals. Extensions to Dirichlet process mixtures and mixtures of skew-elliptical distributions are also discussed.