A Multi-Device Randomized Response Model for Efficient Estimation of Sensitive Attributes

The Randomized Response Technique (RRT), first introduced by Warner, has become a fundamental approach for estimating sensitive characteristics while ensuring respondent anonymity. Over time, enhancements such as the two-device design by Mangat and Singh have improved both the protection of privacy and the accuracy of estimators. Building on this groundwork, the present research proposes a new RRT model that incorporates multiple randomization devices, providing greater flexibility in balancing efficiency with privacy preservation. Theoretical properties of the model are developed, and criteria for efficiency comparison are established. Numerical analyses are conducted, with special emphasis on scenarios involving three randomization devices. In addition to efficiency improvements, the use of layered randomization fosters greater respondent confidence, thereby increasing the likelihood of truthful responses. Overall, the proposed model offers a practical and reliable advancement in sensitive data collection methodologies, with promising applications in social, health, and behavioral research.