Robustness Aspects of Score Tests for Generalized Linear and Partially Linear Regression Models

Robustness aspects of score tests for the null hypothesis of no z effect on the mean response μ for some given subset of explanatory variables, z, are explored in the context of regression analysis. The model considered here is θ = θ(μ) = something else + f(β1z′), where θ is a given transformation of μ via some link function, and f, representing the form of the z effect on θ, is monotonic and twice differentiable. It is shown that the score test for H 0: β1 = 0 remains unchanged whatever the form chosen for f under the alternative, H 1: β1 ≠ 0. This type of robustness is desirable in testing how z might affect the mean response, when precise knowledge of the form for f under H 1 is lacking. Further robust score tests against extreme observations, either in the rank-test sense or in the Hampe–Huber sense, can be achieved for the location family with additive errors, as is pointed out in one of the examples, by replacing in the tests the score vector based on the observations by that based on the ranks or some suitable ψ function. Finally, the simplicity of score tests in seemingly complicated practical situations, a consequence. of their robustness, is demonstrated via testing host variability in dilution experiments.