In this article, we aim to examine an important issue in analyzing binomial response data, i.e., whether the model adequacy and variable selection are robust to the choice of links. We first provide an overview of several commonly used links such as the probit, Jogit, t3-link, complementary log-log link, and Stukel's generalized logistic models. Then, we conduct several comprehensive simulation studies to study whether the choice of links has any impact on model fitting or prediction. Three real data sets are also analyzed in detail. Our simulation study and the real data analysis empirically demonstrate that a wrong choice of links can lead to an underfit or overfit. Thus, a wrong decision can be made if the link function is misspecified. In addition, we also find that variable selection can be sensitive to certain links. However, the Stukel's link is more robust than the other links under consideration.
