A General Class of Nonparametric Models for Ordinal Categorical Data

This paper presents a general class of models for ordinal categorical data that can be specified by means of linear and/or log-linear equality and/or inequality restrictions on the (conditional) probabilities of a multiway contingency table. Some special cases are models with ordered local odds ratios, models with ordered cumulative response probabilities, order-restricted row association and column association models, and models for stochastically ordered marginal distributions. A simple unidimensional Newton algorithm is proposed for obtaining the restricted maximum-likelihood estimates. In situations in which there is some kind of missing data, this algorithm can be implemented in the M step of an EM algorithm. Computation of p-values of testing statistics is performed by means of parametric bootstrapping.