An Improved Quantitative Optional Randomised Response Technique with Additive Scrambling using Two Questions Approach

Abstract

In this paper, an improved two-stage and three-stage optional randomized response (ORR) models for quantitative variables that make the use of additive scrambling was proposed. These two-stage and three-stage models achieve efficient estimation of the mean and sensitivity level simultaneously in the single sample by using two questions. It is found that the proposed models perform better than the existing ORR models in terms of estimating sensitive attribute and sensitivity level simultaneously. It is found that the proposed three stage ORR model provides better estimates than the two-stage and one-stage ORR models and offers more privacy to the respondents with suitable choice of design parameters. The properties of the proposed models are demonstrated with the help of a numerical study.