Principal components adjusted variable screening

Marginal screening has been established as a fast and effective method for high dimensional variable selection method. There are some drawbacks associated with marginal screening, since the marginal model can be viewed as a model misspecification from the joint true model. A principal components adjusted variable screening method is proposed, which uses top principal components as surrogate covariates to account for the variability of the omitted predictors in generalized linear models. The proposed method is demonstrated with superior numerical performance compared with the competing methods. The efficiency of the method is also illustrated with the analysis of the Affymetrix genechip rat genome 230 2.0 array data and the European American SNPs data.