New Randomised Response Models for Two Sensitive Characteristics: Theory and Application

In this paper, we introduce two new randomised response models for estimating the prevalence of two sensitive characteristics and their overlap in a population by making use of a single deck of cards. The proposed models ensure the privacy of the respondents and also reduce the burden on the respondents as they require the random selection of only one card from a deck of cards each of which contains a pair of questions that are to be answered in order. The variance expressions of the proposed estimators are derived and matched to their Cramer-Rao lower bounds of variances. A simulation study has been carried out to compare the proposed models to each other for least protection. Lastly, a real survey application, related to the acceptability of the vaccines produced by Pfizer and Moderna is included. We had findings in Summer 2021 similar to those of the Harvard Study done in December 2021, which was based on a half-million data values, that shows the cost effectiveness of the survey design.

Automated summary

This paper introduces two new randomised response models that use a deck of cards to estimate the prevalence and overlap of sensitive characteristics in a population. These models ensure respondent privacy and reduce respondent burden by randomly selecting one card from a deck, each with a pair of sequential questions. The proposed estimators' variance expressions are derived and matched to their Cramer-Rao lower bounds. A simulation study compares the models for least protection, and a real survey application on vaccine acceptability is included, showing cost effectiveness similar to a Harvard Study.