ONE-SIDED TESTS IN GENERALIZED LINEAR-MODELS WITH PARALLEL REGRESSIONLINES

Likelihood ratio tests for two general one-sided hypotheses in general ized linear models with parallel regression lines are discussed in thi s paper. This kind of model may be interpreted as a generalization of the Finney's (1971, Probit Analysis. Cambridge: Cambridge University P ress) model for simple similar action between two or more compounds. I n particular, for some balanced studies, it is shown that the asymptot ic null distributions do not depend on the parameters and have the sam e size for a class of ordered hypotheses for the potencies. The conven tional distribution theory of the likelihood ratio test does not hold in these cases. For the practical situations of simple order and simpl e tree order, the asymptotic null distributions reduce to the <(chi)ov er bar>(2) distribution. A power study is also conducted in order to c ompare the likelihood ratio tests against ordered and different potenc ies. Finally, we present an illustrative example where the direction o f the antagonism between two insecticides is investigated by comparing the relative potencies of their mixtures.