JSM 2005 - Toronto

Abstract #302304

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 45
Type: Invited
Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #302304
Title: A Bayesian Analysis of Two-way Categorical Data from Small Areas Incorporating Intraclass Correlation
Author(s): Balgobin Nandram*+ and Jai W. Choi
Companies: Worcester Polytechnic Institute and National Center for Health Statistics
Address: Department of Mathematical Sciences, Worcester, MA, 01609,
Keywords: Bayes factor ; Clustered data ; Gibbs sampler ; Hierarchical Bayesian model ; Surrogate sampling
Abstract:

It is straight forward to analyze data from several two-way categorical tables when each table represents data from an area. For each table, the common chi-squared test of independence between the two variables and maximum likelihood estimators of the cell probabilities are readily available. However, when the counts in the two-way categorical tables are formed from familial data (clusters of correlated data), the common chi-squared test no longer applies and the cell probabilities cannot be efficiently estimated. We consider the situation in which the intraclass correlation varies with the size of the cluster, but it is the same for all clusters of the same size. In addition, when the data from each table are sparse, inference for many of the individual tables become inefficient. Our method, an extension of the one in Nandram and Choi (2004) for a single area, permits a ``borrowing of strength'' across the tables via a hierarchical Bayesian model. It is assumed the intraclass correlations and the cell probabilities vary across areas and that they have the same joint distribution over areas. We use Markov Chain Monte Carlo methods to fit our model.


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