Objective Bayesian Comparison of Order-Constrained Models in Contingency Tables.

In social and biomedical sciences, testing in contingency tables often involves order restrictions on cell\r\nprobabilities parameters. We develop objective Bayes methods for order-constrained testing and model\r\ncomparison when observations arise under product binomial or multinomial sampling. Specifically, we\r\nconsider tests for monotone order of the parameters against equality of all parameters. Our strategy\r\ncombines in a unified way both the intrinsic prior methodology and the encompassing prior approach in\r\norder to compute Bayes factors and posterior model probabilities. Performance of our method is evaluated\r\non several simulation studies and real datasets.