Variable Selection Methods Via The Elastic Net In Generalized Linear Models

Variable selection is an extremely important part of statistical modeling, the pre-decessors have done a lot on variable selection in the linear models. The Lasso which is proposed by Tibshirani is especially noticeable, it can do both variable selection and parameter estimate simultaneously. Because its efficient algorithm LARS's proposes, Lasso and its related corrective method research became a popular question in statistics educational world. Elastic Net is one of the corrective method, it is obvious better than Lasso in microarray data analysis. When the variables have group effect in our research data, Elastic Net can select all off them. We apply this method in generalized linear model, popularize this property of Elastic Net estimate for Logistic model and Poisson model. We proved that when there exist group effect in these two kind of models, this method may select completely the group variable too. In addition, we use simulation studies and real data examples show that the Elastic Net outperforms the Lasso and Ridge method.In section 1 we review the development of ordinary linear model and the gener-alized linear model in variable selection aspect research.In section 2 introduce some related preparation knowledge for the generalized linear model and Elastic Net method. In section 3 and 4, we apply Elastic Net in the Logistic model and Poisson model sepa-rately, and give the definition of the Elastic Net estimate and discussed the group effect nature. Simulation and real data are used to illustrate and confirmation. At last, we summarize the full text and propose some questions for further study.