A randomized response model for sensitive attribute with privacy measure using Poisson distribution

In sample surveys, when we need information regarding rare sensitive issues which people often do not prefer to share with others. In such situations this is also awkward for interviewers to ask the direct questions related to confidential and private matters of interviewees. An approach towards the open queries about sensitive issues generally results in the high non-response rates or misleading answers. The aim of this paper is to develop an effective randomized response model to overcome with these types of challenges arising due to sensitive nature of characteristic under study. In this paper we have proposed three-stage randomized response model for estimating mean number of individuals who possessed rare sensitive attribute which makes use of Poisson distribution. The properties of the proposed estimation procedures have been deeply examined when the parameter of a rare unrelated attribute is known as well as unknown. Privacy protection of respondents is also an equally important matter of concern. So measure of privacy protection for the proposed randomized response model has also been examined. Empirical studies are performed to support the theoretical results, which show the dominance of the proposed estimators over well-known contemporary estimators. From the findings of this study we may conclude that proposed randomized response model is rewarding in terms of percent relative efficiencies and privacy protection and may be recommended to survey practitioners for real life applications.