Improved Score Tests for Generalized Linear Models

SUMMARY We present, in matrix notation, an asymptotic expansion for the null distribution of the score statistic in generalized linear models, corrected up to order n −1 where n is the sample size. The expansion has advantages for numerical purposes because it requires only simple operations on matrices. It is also sufficiently simple to be used analytically to obtain several closed form expressions, analogous to Bartlett corrections, in a variety of important score tests. Improved score tests for these models are discussed and various applications to some special tests are given. We show by simulation that two asymptotically equivalent adjusted score tests seem to improve, at least for continuous data, on the usual score test.