Bayesian Test of Quasi-Independence in a Sparse Two-Way Contingency Table Kwak, Sang-Gyu; Kim, Dal-Ho;
We consider a Bayesian test of independence in a two-way contingency table that has some zero cells. To do this, we take a three-stage hierarchical Bayesian model under each hypothesis. For prior, we use Dirichlet density to model the marginal cell and each cell probabilities. Our method does not require complicated computation such as a Metropolis-Hastings algorithm to draw samples from each posterior density of parameters. We draw samples using a Gibbs sampler with a grid method. For complicated posterior formulas, we apply the Monte-Carlo integration and the sampling important resampling algorithm. We compare the values of the Bayes factor with the results of a chi-square test and the likelihood ratio test.
Bayes factor;chi-squared test;likelihood ratio test;quasi-independent;zero cells;
Agresti, A. (2002). Categorical Data Analysis, 2nd Ed., Willey, New York.
Baker, R. J., Clarke, M. R. B. and Lane, P. W. (1985). Zero entries in contingency tables, Computational Statistics and Data Analysis, 3, 33-45.
Bishop, Y. M. M., Fienberg, S. E. and Holland, P. W. (1975). Discrete Multivariate Analysis, MIT Press, Cambridge, MA.
Brown, M. B. and Fuchs, C. (1983). On maximum likelihood estimation in sparse contingency tables, Computational Statistics and Data Analysis, 1, 3-15.
Francoise, V. (1999). StatNews, 01, Spare Contingency Tables, Cornell Statistical Consulting Unit.
Kass, R. E. (1993). Bayes factors in practice, Statistician, 42, 551-560.
Kass, R. E. and Raftery, A. E. (1995). Bayes factor, Journal of the American Statistical Association, 90, 773-795.
Robert, C. P. and Casella, G. (1999). Monte Carlo Statistical Methods, Springer, New York.