Improved wrong-model inference for generalized linear models for binary responses in the presence of link misspecification

In the framework of generalized linear models for binary responses, we develop parametric methods that yield estimators for regression coefficients less compromised by an inadequate posited link function. The improved inference are obtained without correcting a misspecified model, and thus are referred to as wrong-model inference. A byproduct of the proposed methods is a simple test for link misspecification in this class of models. Impressive bias reduction in estimators for the regression coefficients from the proposed methods and promising power of the proposed test to detect link misspecification are demonstrated in simulation studies. We also apply these methods to a classic data example frequently analyzed in the existing literature concerning this class of models.