Bayesian and Maximum Likelihood Approaches to Order-Restricted Inference for Models for Ordinal Categorical Data

Abstract

A class of association models for contingency tables has parameters that are sometimes interpreted as category scores. For classifications having ordered categories, it is often reasonable to assume that the score parameters have a corresponding ordering. This article proposes order-restricted estimates of score parameters in these models. For these estimates, the local log odds ratios have uniform sign. For the Bayesian approach proposed here, prior distributions can induce the order restriction, and prior beliefs reflecting strong association have the effect of moving the estimates away from the boundary of the restricted parameter space. The orderrestricted maximum likelihood solution is obtained in the limit as the prior standard deviation for the strength of association parameter grows unboundedly.

AMS 1980 subject classifications: 62H17, 62A15.

Research partially supported by grant R01 GM33210 of the National Institutes of Health for Dr. Agresti and grant CA11198 of the National Cancer Institute for Dr. Chuang.