Bayesian analysis of optional unrelated question randomized response models

Abstract

The randomized response technique (RRT) is an effective method designed to obtain the sensitive information from respondents while assuring the privacy. Narjis and Shabbir [Narjis, G., and J. Shabbir. 2018. Estimation of population proportion and sensitivity level using optional unrelated question randomized response techniques. Communications in Statistics – Simulation and Computation 0 (0):1–15] proposed three binary optional unrelated question RRT models for estimating the proportion of population that possess a sensitive characteristic $(\pi )$ and the sensitivity level $(\omega )$ of the question. In this study, we have developed the Bayes estimators of two parameters $(\pi ,\omega )$ for optional unrelated question RRT model along with their corresponding minimal Bayes posterior expected losses (BPEL) under squared error loss function (SELF) using beta prior. Relative losses, mean squared error (MSE) and absolute bias are also examined to compare the performances of the Bayes estimates with those of the classical estimates obtained by Narjis and Shabbir (2018). A real survey data are provided for practical utilizations.

Keywords:

• Randomized response
• optional unrelated question
• mean squared error
• Beta prior
• posterior distribution

AMS 2010 SUBJECT CLASSIFICATION:

• 62D05
• 62F15

Acknowledgments

The authors are thankful to the anonymous learned referees for their valuable suggestions to improve the quality of this work.