On Generalized Additive Scrambled Response Modeling in Sensitive Surveys

Abstract

In this article, we use additive scrambling to estimate the mean of a sensitive variable. In the proposed scrambling model, taking G (>1 ) as a positive integer chosen by the interviewer, each respondent is asked to randomly draw G values from a given distribution of scrambling variable and add average of these randomly drawn values to his/her true response on the sensitive variable. Using repetition of the scrambling experiment, we propose a relatively more efficient estimator of sensitive mean without incurring any additional sampling cost. We present a generalization of additive scrambled response models and show that most of additive scrambling models are special cases of suggested generalization. Through algebraic and numerical comparisons, superiority of the proposed methodology is established.