Efficient Optional Randomized Response Model for Estimating The Mean of a Sensitive Attribute with Known Sensitivity Level

  • Authors

    • I. B. Okafor Department of Statistics, Covenant Polytechnic, Aba, Abia State, Nigeria
    • A. C. Onyeka Department of Statistics, Federal University of Technology Owerri, Imo State, Nigeria
    • C. J. Ogbonna Department of Statistics, Federal University of Technology Owerri, Imo State, Nigeria
    • C. H. Izunobi Department of Statistics, Federal University of Technology Owerri, Imo State, Nigeria
    • F. C. Okafor Department of Statistics, University of Nigeria, Nsukka, Enugu State, Nigeria‎
    https://doi.org/10.14419/03yt6271

    Received date: November 22, 2025

    Accepted date: January 19, 2026

    Published date: February 8, 2026

  • Mean; Privacy Protection; Scrambling Response; Sensitivity Level; Stochastic Disturbance

  • Abstract

    The paper proposed an efficient optional randomized response model for estimating the mean of a sensitive variable with known sensitivity level. ‎The model introduced a multiplicative stochastic disturbance to further perturb respondents’ responses and offers the respondents the option to ‎either report a scrambled response or report a truthful response based on their perception of question sensitivity. Theoretical analysis confirms ‎that the estimator is unbiased with minimum variance compared to some existing models. Efficiency conditions and privacy metrics were ‎derived. The results of the empirical study show that the proposed model for different design parameter configurations recorded higher relative efficiency and privacy protection level. The log weighted privacy-efficiency measure further validates its robustness and practicality. By ‎and large, the model offers a reliable and flexible framework for collecting sensitive survey data while minimizing the response bias‎.

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