Sparse Laplacian Shrinkage Estimator For Generalized Linear Models

With the arrival of Big Data era,high-dimensional data has appeared in large numbers,and brought challenges to traditional variable selection methods,thus such data has become a hot subject in modern statistics.As a statistical model,generalized linear model is widely used in practice,while few researches have focused on variable selection method and its applications.Therefore this paper introduces a variable selection method with combined penalty function—SLS method and applies it to a generalized linear model—Logistic regression model.With Monte Carlo method,the simulation of SLS is based on three cases:(1)Analyzing the strengths and weeknesses of SLS and MCP when the simulation variables is of weak correlation;(2)Comparing the advantages and disadvantages of SLS and MCP in application to high dimensional data with highly correlated variables;(3)Simulating the effect of variable selection when there are a collinearity among highly correlated variables,then comparing the results with Lasso,Adaptive Lasso,Elastic-net,Adaptive Elastic-net method.The SLS method is calculated with coordinate descent algorithm(CCD),and the parameters are selected with 5-fold cross validation method.The results show that:(1)When applied to both weakly and highly related variables,SLS method is effective and it functions better than MCP in variable selection.(2)In application to variables with multiple collinearity and high correlation,Lasso,Elastic-net,Adaptive Elastic-net and SLS can remove collinear variables from the model,and SLS can select all relevant variables into the model,thus the effect is better than the other four methods.