RANK ORDER TESTS FOR ORDERED CATEGORICAL RESPONSES ASSUMING LATENT CONTINUOUS VARIABLES

Abstract

The ordered categorical response is assumed to be a manifestation of a latent continuous response or trait. The observed category is assumed to indicate the latent class interval in which the latent continuous variable falls. Nonparametric tests for homogeneity of several populations against regression alternatives are discussed. In univariate case, rank order tests are defined by an extension of Rao's criterion and in a similar manner multivariate rank order tests are defined. Large sample distributions and several power properties as well as properties of rank order scores are discussed. It is shown that Rao's criterion gives an asymptotically most powerful test in the class of rank order tests for univariate distributions.