Journal of Statistical Theory and Practice

, Volume 6, Issue 3, pp 417–427 | Cite as

A Three-Stage Optional Randomized Response Model

  • Samridhi MehtaEmail author
  • B. K. Dass
  • Javid Shabbir
  • Sat Gupta


In Gupta et al. (2010; 2011), it was observed that introduction of a truth element in an optional randomized response model can improve the efficiency of the mean estimator. However, a large value of the truth parameter (T) may be needed if the underlying question is highly sensitive. This can jeopardize respondent cooperation. In what we call a “three-stage optional randomized response model,” a known proportion (T) of the respondents is asked to tell the truth, another known proportion (F) of the respondents is asked to provide a scrambled response, and the remaining respondents are instructed to provide a response following the usual optional randomized response strategy where a respondent provides a truthful response (or a scrambled response) depending on whether he/she considers the question nonsensitive (or sensitive). This is done anonymously based on color-coded cards that the researcher cannot see. In this article we show that a three-stage model may turn out to be more efficient than the corresponding two-stage model, and with a smaller value of T. Greater respondent cooperation will be an added advantage of the three-stage model.

AMS Subject Classification



Quantitative sensitive variable Randomized response Split sample Three-stage model 


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Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  • Samridhi Mehta
    • 1
    Email author
  • B. K. Dass
    • 1
  • Javid Shabbir
    • 2
  • Sat Gupta
    • 3
  1. 1.Department of MathematicsUniversity of DelhiDelhiIndia
  2. 2.Department of StatisticsQuad-I-Azam UniversityIslamabadPakistan
  3. 3.Department of Mathematics and StatisticsUniversity of North Carolina at GreensboroGreensboroUSA

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