  Screening before model building is a reasonable strategy to reduce the
dimension of regression problems. Sure independence screening is an efficient
approach to this purpose. It applies the slope estimate of a simple linear
regression as a surrogate measure of the association between the response and
the predictor so that the final model can be built by those predictors with
steep slopes. However, if the response is truly affected by a nontrivial linear
combination of some predictors then the simple linear regression model is a
misspecified model. In this work, we investigate the performance of the sure
independence screening in the view of model misspecification for binary
response regressions. Both maximum likelihood screening and least square
screening are studied with the assumption that predictors follow multivariate
normal distribution and the true and the working link function belong to a
class of scale mixtures of normal distributions.
