Approximation of powers of some tests in one-way MANOVA type multivariate generalized linear model

The test of an equality of expected values of response vectors in one-way MANOVA type multivariate generalized linear models can be based on deviance or score statistic. This paper aims at approximation of the power of these tests under local alternatives. As indicated by presented simulation study, these approximations perform well over a wide range of models and sample sizes. Approximation of the power of these tests based on a noncentral χ2χ2 distribution derived by Fahrmeir [Fahrmeir, L., 1987. Asymptotic testing theory for generalized linear models. Statistics 18 (1), 65–76] is considered for comparison in the simulation study. The approximation derived in this paper performs better for small sample sizes. The simulation study also provides comparison of the considered tests.