An Improved Versatile Optional Randomised Response Technique for Efficient Estimation in Sensitive Surveys

Abstract

Collecting reliable data on sensitive issues remains a major challenge because respondents are often reluctant to provide truthful answers to sensitive quantitative questions or may refuse to respond altogether. Consequently, direct questioning on topics such as drug use, child abuse, sexual harassment, sexual behaviour, and cybercrime frequently produces biased data and unreliable estimates. The randomised response technique (RRT) addresses this challenge by protecting respondents' privacy, thereby encouraging truthful responses while preventing the disclosure of individual information to the researcher or any third party. However, many existing RRT models provide only modest improvements in estimation efficiency. This study proposes an improved, versatile, optional randomised response technique for collecting quantitative sensitive data with enhanced estimation efficiency. The statistical properties of the proposed model, including its estimator, variance, privacy level, and a combined measure of efficiency and privacy protection, are derived. A numerical study based on four real datasets demonstrates that the proposed model consistently outperforms the existing versatile optional RRT model in terms of estimation efficiency while maintaining respondent privacy. The findings suggest that the proposed model offers a more effective approach for conducting quantitative sensitive surveys and can improve the quality of statistical inference in studies involving sensitive characteristics.