A Bayesian Test of Independence in a Two-Way Contingency Table Under Two-Stage Cluster Sampling with Covariates

• Activity Number: 676
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Dilli Bhatta*+
• Companies: Worcester Polytechnic Institute
• Keywords: Surrogate samples ; Bayes factor ; Hierarchical Bayesian Model ; Markov chain ; TIMSS

Abstract

We consider a Bayesian approach to study independence in a two-way contingency table which is obtained from a two-stage cluster sampling design. We study the association between two categorical variables when there are covariates at both unit and cluster levels. The key idea for our Bayesian test of independence is to convert the cluster sample into an equivalent simple random sample which provides a surrogate of the original sample. Then, this surrogate sample is used to compute the Bayes factor to make an inference about independence. We have used a hierarchical Bayesian model to convert the cluster sample into an equivalent simple random sample. We use Markov chain Monte Carlo algorithms (e.g., Gibbs samplers) to fit the model. The method is applied to the Trend in International Mathematics and Science Study (TIMSS) to assess the association between the mathematics and science scores for fourth grade U.S. students.