Bayesian analysis of square ordinal-ordinal tables

We analyse square contingency tables with ordered categories. Assuming that the observed ordinal categorical variables are manifestations of underlying continuous variables, we formulate a model which allows the comparisons of locations and dispersions between variables. We identify the model by imposing stochastic constraints on the thresholds that define the relationship between the observed and the underlying variables. As a result, the underlying continuous variables' location and dispersion parameters which were not estimable before can be estimated by the Bayesian approach. Illustrative examples are given based on several reported data sets.