Analysis of Contingency Tables by Correspondence Models Subject to Order Constraints

Inferential correspondence analysis, which has gained much attention in recent years, is applied here to contingency tables with ordered categories. To reflect such order, the parameters of the underlying correspondence models are constrained to follow the order induced by the categories of the analyzed table. A reparameterization of the correspondence model in terms of a latent variable model is presented. This allows a simple and straightforward use of the EM algorithm to obtain efficient order-restricted estimates. A goodness-of-fit test is also discussed, and an example is analyzed. A small Monte Carlo example is presented.