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SYNOPTIC ABSTRACT
Gupta, Gupta and Singh (2002) introduced an optional randomized response (ORR) model for estimating the mean and the sensitivity level of a sensitive variable. In an ORR model the respondent is asked to provide a scrambled response only if the respondent considers the question sensitive and a truthful response otherwise. The researcher does not know which type of response is provided. The idea is that a question that is sensitive for one person may not be sensitive for another person. Gupta, Shabbir and Sehra (2010) extended this model to a two-stage ORR model where in the first stage a randomly selected proportion (T) of the respondents is asked to provide a truthful response. The rest of the respondents are asked to go to Stage-2 where they respond according to the ORR model. The main focus of this paper is on finding an optimal value of T for which the two-stage model performs better than the corresponding one-stage model.