Multivariate Permutation Tests for Ordered Categorical Data

The main goal of this article is to compare whether different groups with ordinal responses on the same measurement scale satisfy stochastic dominance and monotonic stochastic ordering. In the literature, the majority of inferential approaches to settle the univariate case are proposed within the likelihood framework. These solutions have very nice characterizations under their stringent assumptions. However, when the set of alternatives lie in a positive orthant with more than four dimensions, it is quite difficult to achieve proper inferences. Further, it is known that testing for stochastic dominance in multivariate cases by likelihood approach is much more difficult than the univariate case. This paper intends to discuss the problem within the conditionality principle of inference through the permutation testing approach and the nonparametric combination (NPC) of dependent permutation tests. The NPC approach based on permutation theory is generally appropriate to suitably find exact good solutions to this kind of problems. Moreover, some solutions for a typical medical example are provided.