Estimation Of Binary Logistic Regression Parameters In Sensitive Surveys For A Two-Stage Randomized Response Technique

Abstract

When collecting data on sensitive topics such as abortion, harassment, tax evasion, and income, respondents often provide untruthful answers, leading to biased results. To address this issue, Warner introduced the Randomized Response Technique (RRT) to obtain sensitive information while ensuring respondent privacy. Building on this, Narjis and Shabbir proposed a two-stage RRT to estimate the prevalence of a sensitive attribute. This study extends their two-stage RRT by incorporating covariates through logistic regression to analyze their effect on the sensitive characteristic. Parameters of the logistic regression model are estimated under simple random sampling, and the performance of maximum likelihood estimators is evaluated through simulation.