A HYBRID SAMPLING METHOD FOR THREE-WAY CONTINGENCY TABLES
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We develop an algorithm blending Sequential Importance Sampling (SIS) and Markov Chain Monte Carlo (MCMC) to conduct goodness of fit testing on three-way contingency tables under the no-three-way interaction model. Unlike previous studies, we conduct SIS utilizing the hypergeometric distribution. Further, our hybrid method capitalizes on the positive aspects of SIS and MCMC while reducing their inefficiencies. We demonstrate the algorithm's performance on equal marginal data sets to highlight computational speed and accuracy. We then demonstrate the algorithm in accurately constructing the null distribution for dense tables that satisfy the asymptotic distribution assumptions. With this result in mind, we estimate the null distribution for sparse tables that violate these assumptions. Our hybrid scheme is shown, via simulation, to be more accurate than simply using the asymptotic distribution for sparse tables.
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