Studies On Ordinal Categorical Regression Using Group Lasso

Ordinal categorical explained variables and naturally grouped explanatory variables are common.As for ordinal categorical explained variables,we choose the ordinal regression model in order to take advantage of the sequential information in variables;as for prior grouped explanatory variables,we choose the group variable selection method of Group Lasso to realize the "group in and group out".In this paper,we establish the ordinal regression model based on the Group Lasso,which aims at analyzing the ordinal regression problem where the prior grouping information of the explanatory variables exists.Firstly,based on the most common ordinal regression model——cumulative ratio model,we establish a cumulative ratio model based on the Group Lasso.Then,considering the advantages of the continuation ratio model in dealing with the problem when the explained variable is irreversible ordered,we further establish the continuation ratio model based on the Group Lasso.Then we use R to generate simulation data sets to test the performance of this model and fit the ordinal regression model based on the Group Lasso penalty and the Lasso penalty separately.We assess the performance in both classification accuracy and variable selection accuracy.The results show that the ordinal regression model based on the Group Lasso perform better than based on the Lasso,which shows that for ordinal regression model,when explanatory variables have natural grouping structure,using the Group Lasso penalty to do variable selection can still improve the performance significantly.Finally,to test the performance of this model in practical problems,we apply the model to the survey data of Chinese General Social Survey(CGSS)in 2017 to analyze the influencing factors of gender equality concept.The results show that,in practical problems,this model can still show good variable selection ability and high classification prediction accuracy.