Importance sampling imputation algorithms in quantile regression with their application in CGSS data

Abstract

As a popular sampling tool used for Monte Carlo computing, importance sampling (IS) has been used in a wide variety of application areas recently. In large-scale survey data such as Chinese General Social Survey (CGSS), missing data, a high level of skewness and heteroscedastic variances commonly occur. Most of the existing literatures on survey data analysis focused on modeling the conditional mean without deep investigation about missing data. In this paper, we study an IS imputation algorithm and its modified algorithm with inverse probability weighting arrangement in quantile regression with missing covariates. We make full use of the observed data compared with the existing complete cases analysis and inverse probability weighting method, and also improve the computational efficiency of multiple imputation and EM-based algorithms. The quantile regression framework allows us to obtain an overall picture of covariates’ effects, highlights the changing relationships according to the explored quantile of interest, and solves the problems of skewness and heterogeneity. Through simulation studies, we investigate the performances of both IS and ISW with other existing algorithms. Finally, we apply our algorithms to part of annual income data from CGSS in 2010. We build three kinds of quantile regression models based on all the subjects, urban areas subjects and rural areas subjects, respectively.