title: On tests against one-sided hypotheses in some generalized linear models.
abstract: One-sided hypotheses arise naturally in many situations. When testing against such hypotheses, it is desirable to take the available one-sided information into account, rather than simply applying a two-sided test. 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 various tests of one-sided hypotheses in a class of models that includes generalized linear and Cox regression models. The tests are likelihood ratio, Wald, score, generalized distance, and a Pearson chi-square. It is shown that these test statistics are asymptomatically equivalent in terms of local power; this is a generalization of the well-known corresponding result for two-sided alternatives. Two examples are also discussed. They are on (1) testing for interaction in binomial response models, and (2) comparison of treatments with ordinal categorical responses.
authors.affiliation: School of Agriculture, La Trobe University, Bundoora, Australia.
authors.forename: M J
authors.initials: MJ
authors.lastname: Silvapulle
mesh_terms: D000585:Aminacrine / Q000494:pharmacology; D002840:Chromates / Q000494:pharmacology; D004926:Escherichia coli / Q000187:drug effects*; D016014:Linear Models; D008433:Mathematics; D009152:Mutagenicity Tests / Q000379:methods*; D017680:Potassium Compounds / Q000494:pharmacology
chemical_list: D002840:Chromates; D017680:Potassium Compounds; C027373:potassium chromate(VI); D000585:Aminacrine