High dimensional logistic regression model using adjusted elastic net penalty

Reduction of the high dimensional binary classification data using penalized logistic regression is one of the challenges when the explanatory variables are correlated. To tackle both estimating the coefficients and performing the variable selection simultaneously, elastic net penalty was successfully applied in high dimensional binary classification. However, elastic net has two major limitations. First it does not encourage grouping effects when there is no high correlation. Second, it is not consistent in variable selection. To address these issues, an adjusted of the elastic net (AEN) and its adaptive adjusted elastic net (AAEM), are proposed to take into account the small and medium correlation between explanatory variables and to provide the consistency of the variable selection simultaneously. Our simulation and real data results show that AEN and AAEN have advantage with small, medium, and extremely correlated variables in terms of both prediction and variable selection consistency comparing with other existing penalized methods.