Variable Screenings in Binary Response Regressions with Multivariate Normal Predictors

Abstract: 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.