Analysis of Treatment Response Data without the Joint Distribution of Counterfactuals

• Activity Number: 212
• Type: Topic Contributed
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Siddhartha Chib*+
• Companies: Washington University, St. Louis
• Keywords: Bayesian inference ; instrumental variable ; Metropolis-Hastings algorithm ; observational data ; potential outcomes ; treatment effect

Abstract

This talk is concerned with the Bayesian analysis of treatment response data when the (categorical) treatment is nonrandomly assigned but a binary instrumental variable is available, say from the design of the problem. We show that unlike previous work it is possible to analyze this problem without the modeling of the joint distribution of the counterfactuals. The modeling and prior-posterior analysis are developed for both binary and ordinal treatments under weak distributional assumptions. Estimation of these models is by Markov chain Monte Carlo methods, after rewriting the models in line with the framework of Albert and Chib (1993), and the comparison of the various models is by marginal likelihoods and Bayes factors, estimated by the method of Chib (1995). We discuss inferences for the treatment effects, outlining ways in which one can calculate the effect of the instrument on the outcome, both from the intrinsic structure of the model and the output of the MCMC simulations. Several illustrations of the methods are provided.