ON TESTS AGAINST ONE-SIDED HYPOTHESES IN SOME GENERALIZED LINEAR-MODELS

One-sided hypotheses arise naturally in many situations. When testing against such hypotheses, it is desirable to take the available one-sid ed information into account, rather than simply applying a two-sided t est. What we expect to gain by applying a one-sided test instead of a two-sided test is an increase in the power of the test. We consider va rious tests of one-sided hypotheses in a class of models that includes generalized linear and Cox regression models. The tests are likelihoo d ratio, Wald, score, generalized distance, and a Pearson chi-square. It is shown that these test statistics are asymptotically equivalent i n terms of local power; this is a generalization of the well-known cor responding result for two-sided alternatives. Two examples are also di scussed. They are on (1) testing for interaction in binomial response models, and (2) comparison of treatments with ordinal categorical resp onses.