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

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.