Model Checking for Logistic Models When the Number of Parameters Tends to Infinity

We propose a projection-based test to check logistic regression models when the dimension of the covariate vector may be divergent. The proposed test achieves a reduction in dimension, and the proposed method behaves as if only a single covariate is present. The test is shown to be consistent and can detect root-n local alternatives. We derive the asymptotic distribution of the proposed test under the null hypothesis and establish the test's asymptotic behavior under the local and global alternatives. The numerical performance is remarkably attractive comparing to the existing methods. Real examples are presented for illustration. Supplementary materials for this article are available online.