In the RC association model for a two-way contingency table, it is often natural to impose order constraints on the score parameters of the row and column variables. In this article, a simple and efficient Bayesian model selection procedure is proposed that simultaneously compares all possible combinations of (in)equalities of successive score parameters in the order restricted RC association model. The method introduces normal latent variables into the model and uses a simple and accurate approximation to the likelihood function so that the full conditional posterior distributions of elements of the parameter are given as truncated normal distributions. The Gibbs sampling algorithm of Gelfand and Smith (1990) is employed to generate samples from the full model in which all the scores are strictly ordered, and posterior probabilities of all possible models are estimated by using the Gibbs output from the full model. A simulation study shows that the proposed method performs well in detecting the true model. Two real data sets are analyzed using the proposed method.
- Contingency tables
- Inequality constraints
- Markov chain Monte Carlo
- Model selection
- Ordinal categorical variables