Exact Inference for Three-way Interaction Effects

Abstract

The contingency table analysis is generally based on the log-linear model conditioning on sufficient statistics. We can easily design algorithms to maintain these conditions, but it is often very difficult to ensure irreducibility, particularly, in no three-way interaction test. Recently, Cheon (2012) applied the stochastic approximation Monte Carlo algorithm (SAMC, Liang et al., 2007) to approximate the exact test of mutual independence in multiway contingency table. In this paper, we propose a method using SAMC to approximate the exact test for the contingency table as a test of the null hypothesis of no three-way interaction among variables. The proposed method avoids reducibility problem and its performance has been investigated on three real datasets, comparing with existing importance sampling and Markov chain Monte Carlo methods. The numerical results are in favor of our method in terms of quality of estimates.