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 theproposed scrambling model, taking G (>1 ) as a positive integer chosen by the interviewer, eachrespondent is asked to randomly draw G values from a given distribution of scrambling variableand 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 estimatorof sensitive mean without incurring any additional sampling cost. We present a generalization ofadditive scrambled response models and show that most of additive scrambling models are specialcases of suggested generalization. Through algebraic and numerical comparisons, superiority ofthe proposed methodology is established.