On Randomized Response Surveys of Binary Characteristics Using Polychotomous Response Variables

The randomized response (RR) procedures for estimating the proportion (π) of a population belonging to a sensitive or stigmatized group ask each respondent to report a response by randomly transforming his/her true attribute into one of several response categories. In this paper, we present a common framework for discussing various RR surveys of dichotomous populations with polychotomous responses. The unified approach is focused on the substantive issues relating to respondents’ privacy and statistical efficiency and is helpful for fair comparison of various procedures. We describe a general technique for obtaining unbiased estimators of π based on RR data, from unbiased estimators of π based on open surveys. The technique works well for any sampling design p(s) and also for variance estimation. We develop an approach for comparing RR procedures, taking both respondents’ protection and statistical efficiency into account. For any given RR procedure with three or