Estimation of population proportion and sensitivity level using optional unrelated question randomized response techniques

Abstract

In this study, we propose optional randomized response technique (RRT) models in binary response situation. Gupta, Gupta, and Singh (2002) introduced the basic premise of optional RRT model, that a question may be sensitive for one respondent but may not be sensitive for another. In an optional RRT model, a respondent is requested to provide a scrambled response only if he/she considers the question is sensitive. Otherwise, the respondent provides a truthful response. This study focus on estimating π, the prevalence sensitive characteristics, and ω, the sensitivity level of the underlying sensitive question. Two-question and split-sample approaches are used for parameters $(\pi ,\omega )$ estimation. A comparison between proposed optional RRT models and corresponding full RRT models are carried out numerically.

Keywords:

• Two-question approach
• Split-sample approach
• Optimal allocation of sample sizes
• Randomized response

Acknowledgments

Authors are thankful to the anonymous referee for his valuable suggestions regarding improvement of paper.