Variable Selection for Generalized Linear Model with Highly Correlated Covariates

The penalized variable selection methods are often used to select the relevant covariates and estimate the unknown regression coefficients simultaneously, but these existing methods may fail to be consistent for the setting with highly correlated covariates. In this paper, the semi-standard partial covariance (SPAC) method with Lasso penalty is proposed to study the generalized linear model with highly correlated covariates, and the consistencies of the estimation and variable selection are shown in high-dimensional settings under some regularity conditions. Some simulation studies and an analysis of colon tumor dataset are carried out to show that the proposed method performs better in addressing highly correlated problem than the traditional penalized variable selection methods.