Order-restricted inference for monotone trend alternatives in contingency tables

For many contingency tables with ordered categories, one expects a monotone association yet one may prefer not to assume a particular parametric model. This article presents estimation and likelihood-ratio testing for various monotone trend alternatives to independence in such tables. The alternatives are characterized by non-negative values for four types of log odds ratios for ordinal data: Local, global, cumulative, and continuation-ratio. When monotone association exists according to all these criteria, tests based on local odds ratios are asymptotically more powerful than tests with odds ratios having greater aggregation. Sampling distributions of these test statistics are awkward even for large samples, but it is straightforward to simulate their exact distributions and provide nearly exact P-values. Extensions are given to order restricted inference about conditional association in a three-way contingency table and about marginal distributions of a square contingency table. The analyses presented here have the advantage of weaker assumptions than those based on parametric models, but research is needed to study conditions under which they are more or less powerful than the model-based methods. (C) 1998 Elsevier Science B.V. All rights reserved.