Additive Randomized Response Model with Known Sensitivity Level

Abstract

Randomized Response Technique (RRT) is an indirect survey method to collect sensitive information from the respondent without unveiling his/her true status. RRT has been first developed by Warner [12]. Tiwari & Mehta [11] proposed a model in which sensitivity level was taken as a known quantity under the assumption that if the respondent did not feel that the survey question was sensitive and can give an honest answer frankly, then it was not needed to conceal his/her identity and we can receive the true response from them without applying the randomization techniques. In this article, the idea of known sensitivity level proposed by Tiwari & Mehta [11] has been applied to One-Stage Optional Randomized Response Technique (ORRT) (Gupta et al. [5]), Two-Stage Optional Randomized Response Technique (ORRT) (Gupta et al. [6]) and Three-Stage Optional Randomized Response Technique (ORRT) (Mehta et al. [9]) based on quantitative data. The variances of the mean estimators of the models with sensitivity level considered as known, have been compared with the variances of the mean estimators of the models with unknown sensitivity level for all the above three models. It has been empirically established that the relative efficiency (RE) of the mean estimator for proposed model with known sensitivity level as compared to the RE of the mean estimator for the models with unknown sensitivity level was found to be greater than one for all the different cases considered by us. The proposed model is also simpler for use, as only one sample is required in it for collecting the sensitive information.