Exact inference in contingency tables via stochastic approximation Monte Carlo

Monte Carlo methods for the exact inference have received much attention recently in complete or incomplete contingency table analysis. However, conventional Markov chain Monte Carlo, such as the Metropolis–Hastings algorithm, and importance sampling methods sometimes generate the poor performance by failing to produce valid tables. In this paper, we apply an adaptive Monte Carlo algorithm, the stochastic approximation Monte Carlo algorithm (SAMC; Liang, Liu, & Carroll, 2007), to the exact test of the goodness-of-fit of the model in complete or incomplete contingency tables containing some structural zero cells. The numerical results are in favor of our method in terms of quality of estimates.