Abstract: As a useful generalization, Stukel generalized logistic models can fit binary response variable more flexibly and conveniently comparing to other generalizations. In this paper, we propose a projection-based test to check Stukel models. The test is shown to be consistent and can detect root-n local alternative hypotheses, and can be used to check the standard logistic models as well. We establish the asymptotic distribution of the proposed test under the null hypothesis and analyze asymptotic properties under the local and global alternatives. We evaluate the finite-sample performance via simulation studies and apply the proposed method to analyze a real dataset as an illustration.

Key words and phrases: Consistent test, generalized logistic models, marked empirical process, projection.