关键词: 变量选择, 群组变量, 惩罚似然, 信用评分

Abstract: Variable selection is of great importance in statistical modeling. Suitable variables can make the model simple and have favorite performance of prediction. We propose a novel penalized bi-level variable selection method——adaptive Sparse Group Lasso (adSGL), under the framework of logistic regression. Its uniqueness is that it does selection based on the grouping structure of predictors, which realizes selections at both group and individual level. It has the advantage of allowing different amounts of shrinkage for different individuals and groups, which can avoid over shrinkage for large coefficients and improve the accuracies of estimate and prediction. The difficulties of solution lies in the non-strict convexity of the penalized likelihood function so we solve the model based on block coordinate descent and establish selection criteria of tuning parameter. Simulation studies show that in compare with three representative methods Sparse Group Lasso、Group Lasso and Lasso, adSGL not only enhances bi-level selection accuracy, but also reduces model error. In the application of credit card credit scoring dataset shows that in compare with logistic regression，adSGL method has higher classification accuracy and better robustness.

Key words: Variable Selection, Grouped Variables, Penalized Likelihood, Credit Scoring