Computing Exact Distributions for Polytomous Response Data

Abstract This article presents an efficient method for computing exact conditional distributions of the sufficient statistics for the parameters of four polytomous response models. For nominal response, two baseline category logit models and, for ordinal response, two adjacent categories logit models are considered. The method consists of recursive generation of the joint distribution of the sufficient statistics, augmented by a technique to slice off portions of the evolving sample space so as to eventually yield the required conditional distribution. Two actual data sets are analyzed to illustrate the method.