Estimating the prevalence of sensitive attribute with optional unrelated question randomized response models under simple and stratified random sampling

Document Type : Article

Authors

Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan

Abstract

In this study, we propose optional randomized response technique (RRT) models in binary response situation. The utility of proposed optional RRT models under stratification are also explored. Gupta et al.\cite{Singh} introduced an ingenious idea of optional RRT model, that a question may be sensitive for one respondent but may not be sensitive for another. This study focus on estimating $ \pi $, the prevalence of sensitive attribute, $ \omega $, the sensitivity level of the underlying sensitive question when the proportion of unrelated innocuous attribute $ \pi_{{x}} $ is unknown. A new multi-question approach are proposed and used for estimation of parameters $ (\pi,\omega) $. A comparison between proposed optional RRT models and corresponding full RRT models are carried out numerically under simple and stratified random sampling.

Keywords


References
[1] Gupta, S. N., Gupta, B. C. and Singh, S.“Estimation of sensitivity level of personnel interview
survey questions”, Journal of Statistical Planning and Inference, 100, pp. 239–247 (2002).
[2] Warner, S. L. “Randomized response: A survey technique for eliminating evasive answer
bias”, Journal of the American Statistical Association, 60(309), pp. 63–69 (1965).
[3] Greenberg, B., Abul-Ela, A., Simmons, W. and Horvitz, D. “ The unrelated question randomized response model: theoretical framework”, Journal of the American Statistical Association,
64(326), pp. 520–539 (1969).
[4] Chaudhuri, A. and Mukerjee, R. “Randomized Response: Theory and Techniques”, Marcel
Dekker, Inc (1998).
[5] Mahmood, M., Singh, S. and Horn, S. “ On the confidentiality guaranteed under randomized
response sampling: a comparisons with several techniques”, Biometrical Journal, 40, pp.
237–242 (1998).
23[6] Perri, P. F. “Modified randomized devices for simmons’ model ”, Model Assisted Statistics
and Applications, 3(3), pp. 233–239 (2008).
[7] Hussain, Z. and Shabbir, J.“Estimation of the mean of a socially undesirable characteristic”,
Scientia Iranica , 20(3), pp. 839–845(2013).
[8] Lee, G. S., Hong, K-H., Kim, J-M. and Son, C-K. “An estimation of a sensitive attribute
based on a two stage stratified randomized response model with stratified unequal probability
sampling”, Brazilian Journal of Probability and Statistics, 28 (3), pp. 381-408 (2014).
[9] Abdelfatah, S. and Mazloum, R. “Improved randomized response model using three decks of
cards”, Model Assisted Statistical Application, 9, pp. 63–72 (2014).
[10] Tanveer, T. A. and Singh, H. P. “Some improved additive randomized response models utilizing higher order moments ratios of scrambling variable”, Models Assisted Statistics and
Applications, 10(4), pp. 361–383 (2015).
[11] Singh, H. P. and Tanveer, T. A. “ An Improvement Over Kim and Elam Stratified Unrelated
Question Randomized Response Model Using Neyman Allocation”, Sankhy a: The Indian
Journal of Statistics, 77(B), pp. 91–107 (2015).
[12] Blair, G., Imai, K. and Zhou, Y-Y. “Design and analysis of the randomized response technique”, Journal of the American Statistical Association, 110(511), pp. 1304–1319, (2015).
[13] Singh, H. P. and Gorey, S. M. “An efficient new randomized response model”, Communications in Statistics-Theory and Methods, 46(19), pp. 9629–9635 (2016).
[14] Bose,M. “Respondent privacy and estimation efficiency in randomized response surveys for
discrete-valued sensitive variables", Statistical Papers 56 (4), pp. 1055–1069 (2015).
[15] Abid, M., Naeem, A., Hussain, Z., Riaz, M. and Tahir, M. “Investigating the Impact of Simple
and Mixture Priors on Estimating Sensitive Proportion Through a General Class of Randomized Response Models”, Scientia Iranica ,26(2), pp. 1009–1022 (2019).
[16] Mangat, N. S. and Singh, R.“ An alternative randomized response procedure”, Biometrika,
77(2), pp.439–442 (1990).
24
[17] Gupta, S. and Shabbir, J. “Sensitivity estimation for personal interview survey questions”,
Statistica, 64(4), pp. 643–653 (2004).
[18] Gupta, S., Shabbir, J. and Sehra, S.“Mean and sensitivity estimation in optional randomized
response models”, Journal of Statistical Planning and Inference, 140(10), pp. 2870–2874
(2010).
[19] Gupta, S., Thornton, B., Shabbir, J. and Singhal, S. “ A comparison of multiplicative and
additive optional RRT models”, Journal of Statistical Theory and Applications, 5, pp. 226–
239 (2006).
[20] Gupta, S. N., Tuck, A., T., S. G. and Crowe, M. “ Optional unrelated question randomized
response models”, Involve: A Journal of Mathematics, 6(4), pp. 483–492 (2013).
[21] Chhabra, A., Dass, B., and Mehta, S.“ Multistage optional unrelated question RRT model”,
Journal of Statistical Theory and Applications, 15(1), pp. 80–95 (2016).
[22] Gupta, S., Shabbir, J. and Kalucha, G. “A two-step approach to ratio and regression estimation
of finite population mean using optional randomized response models ”, Hacettepe Journal
of Mathematics and Statistics, 45(06), pp. 1819–1830 (2016).
[23] Sihm, J. S., Chhabra, A. and Gupta, S. N. “ An optional unrelated question RRT model”,
Involve: A Journal of Mathematics, 9(2), pp. 195–209 (2016).
[24] Narjis, G. and Shabbir, J. “Estimation of population proportion and sensitivity level using
optional unrelated question randomized response techniques”, Communications in Statistics
- Simulation and Computation, 0(0), pp. 1–16 (2018), doi: 10.1080/03610918.2018.1538453.
[25] Lanke, J. “On the degree of protection in randomized interviews”, International Statistical
Review, 44, pp. 197–203 (1976)