Parametric and Nonparametric Bayesian Modeling for Ecological Inference in 2\times 2 Tables: A Data Augmentation Approach

• Activity Number: 199
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Kosuke Imai*+ and Ying Lu
• Companies: Princeton University and Princeton University
• Keywords: ecological regression ; racial voting ; Dirichlet process prior ; nonparametric methods ; aggregate data ; missing data

Abstract

The ecological inference problem arises when one wishes to make inferences about individual behavior from aggregate level data. Such a situation is frequently encountered in the social sciences and epidemiology. We propose a general framework for ecological inference based on data augmentation. Ecological inference in 2 \times 2 tables is formulated as a missing data problem where only the weighted sum of the two unknown variables is observed. Following the existing literature, our first approach uses a parametric model to impute the missing data. We show how this model can be extended to incorporate covariate information as well as any hierarchical structure that may exist in the data. To overcome the limitation of parametric assumptions, we also develop a nonparametric model, which is based on a mixture of Dirichlet processes. This nonparametric model offers the advantage of greater flexibility to estimate the distribution of the unknown parameters. Finally, through simulation studies and empirical illustrations, we evaluate the performance of the parametric and nonparametric models in the presence of various degrees of aggregation bias.