Abstract #300217

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JSM 2003 Abstract #300217
Activity Number: 52
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
Sponsor: Section on Survey Research Methods
Abstract - #300217
Title: A Bayesian Alternative to the Chi-Squared Test of Association in a Two-Way Categorical Table with Intraclass Correlation
Author(s): Jai Won Choi*+ and Balgobin Nandram
Companies: Centers for Disease Control and Prevention and Worcester Polytechnic Institute
Address: 9504 Mary Knoll Dr., Rockville, MD, 20850-3469,
Keywords: Bayes factor ; Gibbs sampler ; Monte Carlo integration ; multinomial-Dirichlet
Abstract:

It is straightforward to analyze data from a single multinomial table. Specifically, for the analysis of a two-way categorical table, the common chi-squared test of independence between the two variables and maximum likelihood estimators are readily available. When the counts in the two-way categorical table are formed from familial data (clusters of correlated data), the issue becomes complex and the common chi-squared test no longer applies. We note that there are several approximate adjustments to the common chi-squared test. However, our main contribution is the construction and analysis of a Bayesian model which removes all analytical approximations. This is an extension of a standard multinomial-Dirichlet model to include the intraclass correlation associated with the individuals within a cluster. This intraclass correlation varies with the size of the cluster, but it is the same for all clusters of the same size. We use Markov chain Monte Carlo methods to fit our model, and to make posterior inference about the intraclass correlations and the the cell probabilities. Also, using Monte Carlo integration with a binomial importance function (a clever choice), we obtain the Bayes factor for a test of no association.

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