Regression and Ordered Categorical Variables

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Abstract
A general approach to regression modelling for ordered categorical response variables, y, is given, which is equally applicable to ordered and unordered y. The regressor variables xT = (x1,…,xp) may be continuous or categorical. The method is based on the logistic family which contains a hierarchy of regression models, ranging from ordered to unordered models. Ordered properties of the former, the stereotype model, are established. The choice between models is made empirically on the basis of model fit. This is particularly important for assessed, ordered categorical response variables, where it is not obvious a priori whether or not the ordering is relevant to the regression relationship. Model simplification is investigated in terms of whether or not the response categories are distinguishable with respect to x. The models are fitted iteratively using the method of maximum likelihood. Examples are given.