Bayesian inference for marginal models under equality and inequality constraints

We develop a Bayesian framework for making inference on a class of marginal models for categorical variables, which is formulated through equality and/or inequality constraints on generalized logits, generalized log-odds ratios and similar higher-order interactions. A Markov chain Monte Carlo (MCMC) algorithm is used for parameters estimation and for computing the Bayes factor between competing models. The approach is illustrated through the application to a well-known dataset on social mobility.