Sampling estimating equation for logistic regression with multi-dimensional missing binary covariates: application to a divorce data

Abstract

This paper focuses on analysing a divorce data collected in Sichuan Province, China. The responses of this divorce data are binary variables. Among 17 covariates, there are 12 binary variables with missing values. Thus, the vectors of covariates with missing values are multi-dimensional and have binary components. Existing approaches usually focus on one-dimensional binary covariates and therefore cannot deal with this divorce data. To figure out multi-dimensional binary covariates, a sampling estimating equation based on the logistic regression and sampling the missing binary covariates are proposed. Statistical inference based on this sampling estimating equation is presented. This paper has two main contributions. First, the proposed sampling estimating equation is able to obtain reasonable parameter estimators under multi-dimensional missing binary covariates setting, which cannot be handled by existing approaches. Second, for two-category problem, subjects with multi-dimensional missing binary covariates can be classified efficiently, which is intractable for existing approaches. Real data analysis of the divorce data reveals profound results for the divorce cases in Sichuan Province. The proposed sampling estimating equation performs well in terms of classification and prediction on this divorce data.