IMPROVED SCORE TESTS FOR GENERALIZED LINEAR-MODELS

We present, in matrix notation, an asymptotic expansion for the null d istribution of the score statistic in generalized linear models, corre cted up to order n-1 where n is the sample size. The expansion has adv antages for numerical purposes because it requires only simple operati ons on matrices. It is also sufficiently simple to be used analyticall y to obtain several closed form expressions, analogous to Bartlett cor rections, in a variety of important score tests. Improved score tests for these models are discussed and various applications to some specia l tests are given. We show by simulation that two asymptotically equiv alent adjusted score tests seem to improve, at least for continuous da ta, on the usual score test.