A general non-parametric approach to the analysis of ordinal categorical data

This paper presents a general class of models for ordinal categorical data which can be specified by means of linear and/or log-linear equality and/or inequality restrictions on the (conditional) probabilities of a multi-way 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 uni-dimensional 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.

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