Additive Optional Scrambled Randomized Response Model for Estimating Population Mean and Sensitivity Level of Sensitive Variable
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.
N. P. Olewuezi
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.
*Author to whom correspondence should be addressed.
Abstract
The paper proposed an additive optional randomized response technique model that improves upon Gjestvang and Singh (2009) model by effectively balancing respondents privacy protection and statistical estimation efficiency. The proposed model establishes an unbiased estimator of the population mean under both simple random sampling and probability proportional to size sampling schemes. The proposed model effectively balances the privacy protection with statistical efficiency – a key trade-off in survey design involving sensitive variable. For all values of scrambling parameters and sensitivity level, the proposed model recorded high gain in efficiency and the relative efficiency of the proposed model under both sampling scheme is greater than one. As sensitivity level increases, the relative gain in efficiency decreases which is in agreement with theoretical expectations. Nevertheless, even at high sensitivity level W = 0.9, the proposed model maintained acceptable efficiency and unbiasedness. The weighted privacy-efficiency measure established that proposed model out-performed Gjestvang and Singh (2009) model.
Keywords: Scrambling randomized response, privacy protection, statistical estimation, mean, sensitive variable