Variable selection and model prediction based on Lasso, adaptive lasso and elastic net

Statistics and modeling is gaining more and more attention as the time for big data is coming. Variable choosing plays a significant role during modeling. The traditional methods like OLS and ridge regression could not satisfy interpretability and prediction accuracy at the same time. Tibshirani. R prompted Lasso and the new method could not only solve the above problem but also decrease the complexity of calculation. The paper aims to compare Lasso and adaptive lasso, elastic net. We do experiment on the classical case?diabetes patient data and choose model with AIC, BIC and cross validation to get the advantage and disadvantage of the above methods. According to the result, we draw the conclusion that Lasso performances better in variable selection, however, the predictions are not as accurate as the other two methods. Adaptive Lasso selects less variables and gives a more accurant prediction value. Elastic net has a most interpretative model.