One-Sided Tests in Generalized Linear Models with Parallel Regression Lines

Abstract

Likelihood ratio tests for two general one-sided hypotheses in generalized linear models with parallel regression lines are discussed in this paper. This kind of model may be interpreted as a generalization of the Finney's (1971, Probit Analysis. Cambridge: Cambridge University Press) model for simple similar action between two or more compounds. In particular, for some balanced studies, it is shown that the asymptotic null distributions do not depend on the parameters and have the same size for a class of ordered hypotheses for the potencies. The conventional distribution theory of the likelihood ratio test does not hold in these cases. For the practical situations of simple order and simple tree order, the asymptotic null distributions reduce to the -2 distribution. A power study is also conducted in order to compare the likelihood ratio tests against ordered and different potencies. Finally, we present an illustrative example where the direction of the antagonism between two insecticides is investigated by comparing the relative potencies of their mixtures.