Latent variable models for ordered categorical data

Abstract The multivariate analysis of ordered categorical data is an important growth point in statistics especially as applied to the social sciences. This paper is concerned with the situation in which the associations between a set of categorical variables are assumed to arise from their dependence on a small number of latent variables. The problem of modelling this relationship is first posed in very general terms and then specialized to particular cases for which statistical methods are available or in course of development. Such models can be viewed as tools for data reduction or for scaling and both aspects are reviewed. The possible relevance of the method in economics and their relationship to other methods for categorical variables is briefly discussed.