A Study on Selection Bias Correction Based on Statistical Decision Theory in Logistic Regression Models

Abstract

Online surveys are very useful for planning and verifying policies in many fields such as marketing because of their high cost-effectiveness and ease. However, due to difficulties to conduct it by random sampling, the survey results often contain selection bias. To cope with this problem, the method has been proposed by modeling the occurrence of selection bias and correcting it based on statistical decision theory. To apply this method to analyzing online surveys, it is necessary to put it into a specific model and examine its performance. In this study, we consider correcting selection bias in online surveys in which the response is binary and covariates are represented by continuous values, and assume logistic regression model as a data generation model. Then, we develop a correction method using a selection bias correction framework based on statistical decision theory. We also clarify its properties in numerical experiments on artificial data.