Two mixed randomized response models under simple and stratied random sampling with replacement schemes

Abstract

We have proposed two mixed randomized response models for surveying sensitive issues. The properties of proposed estimators are derived under the simple and stratified random sampling schemes while considering completely and less than completely truthful reporting cases. We proved that the proposed models are unconditionally efficient than [13, 15, 16, 20]. In order to get the idea of gain in efficiency and model stability numerical and graphical efficiency comparisons are done for the two models under two mentioned cases.

Keywords

• Categorical responses,Randomization,Less than completely truthful reporting,Stratication,Optimum allocation

References

1. Abdelfatah, S., and Mazloum, R. An improved stratied randomized response model using two decks of cards, Model Assisted Statistics and Applications, 10 (4), 309-320, 2015.
2. Al-Menayes, J. Measuring the Spiritual and Behavioral Dimensions of Religiosity in a Mus- lim Sample, Asian Social Science, 12 (2), 158, 2016.
3. Blair, Graeme, Kosuke Imai, and Yang-Yang Zhou. Design and Analysis of the Randomized Response Technique, Journal of the American Statistical Association, 110 (511), 1304 - 1319, 2015.
4. Clark, S. J., and Desharnais, R. A. Honest answers to embarrassing questions: Detecting cheating in the randomized response model, Psychological Methods, 3 (2), 160, 1998.
5. Coutts, E., and Jann, B. Sensitive questions in online surveys: Experimental results for the randomized response technique (RRT) and the unmatched count technique (UCT), Socio- logical Methods and Research, 40 (1), 169-193, 2011.
6. Greenberg, B. G., Abul-Ela, A. L. A., Simmons, W. R. and Horvitz, D. G. The unrelated question randomized response model: Theoretical framework, Journal of the American Sta- tistical Association, 64 (326), 520-539, 1969.
7. Holbrook, A. L., and Krosnick, J. A. Measuring Voter Turnout By Using The Randomized Response Technique Evidence Calling Into Question The Method's Validity Public Opinion Quarterly, 74 (2), 328-343, 2010.
8. Hong, K., Yum, J. and Lee, H. A stratied randomized response technique Korean Journal of Applied Statistics, 7, 141-147, 1994.

9. Jin, Z., Zhu, Z., Yu, B. and Gao, Ge. A Monte Carlo Simulation Investigating the Validity and Reliability of Two Stage Cluster Sampling Survey with Sensitive Topics Computer Modelling and New Technologies, 17 (3), 69 - 75, 2013.
10. Kim, J. M. and Elam, M. E. A two-stage stratied Warner's randomized response model using optimal allocation Metrika, 61 (1), 1-7, 2005.
11. Kim, J. M. and Elam, M. E. A stratied unrelated question randomized response model Statistical Papers, 48 (2), 215-233, 2007.
12. Kim, J. M. and Warde, W. D. A stratied Warner's randomized response model Journal of Statistical Planning and Inference, 120 (1), 155-165, 2004.
13. Kim, J. M. and Warde, W. D. A mixed randomized response model Journal of Statistical Planning and Inference, 133 (1), 211-221, 2005.
14. Locander, W., Sudman, S., and Bradburn, N. An investigation of interview method, threat and response distortion Journal of the American Statistical Association, 71 (354), 269-275, 1976.
15. Mangat, N. S., Singh, R., and Singh, S. Violation of respondent's privacy in moors' model- its rectication through a random group strategy Communications in Statistics-Theory and Methods, 26 (3), 743-754, 1997.
16. Moors, J. A. Optimization of the unrelated question randomized response model, Journal of the American Statistical Association, 66 (335), 627-629, 1971.
17. Nazuk, A. and Shabbir, J. A new mixed randomized response model International Journal of Business and Social Science, 1 (1), 186-190, 2010.
18. Phillips, D. L. Knowledge from what?, Chicago: Rand-McNally, 1971.
19. Singh, S., Singh, R., and Mangat, N. S. Some alternative strategies to Moors' model in randomized response sampling, Journal of Statistical Planning and inference, 83 (1), 243- 255, 2000.
20. Singh, H. P. and Tarray, T. A. An alternative to Kim and Warde's mixed randomized response model, SORT-Statistics and Operations Research Transactions, 1 (2), 189-210, 2013.
21. Singh, H. P. and Tarray, T. A. An alternative to stratied Kim and Warde's randomized response model using optimal (Neyman) allocation, Model Assisted Statistics and Applica- tions, 9 (1), 37-62, 2014.
22. Son, C. K., and Kim, J. M. Bayes linear estimator for two-stage and stratied randomized response models, Model Assisted Statistics and Applications, 10 (4), 321-333, 2015.
23. Soudarssanane, M., Naik, B., Sahai, A., and Bazroy, J. Randomised Response Technique-An Innovative Method To Measure Culturally Sensitive Variables: Results From A Pilot Study, Indian Journal of Community Medicine, 28 (3), 138, 2003.
24. Stem, D. E., and Bozman, C. S. Respondant Anxiety Reduction with Randomized Response Technique, Advanced in consumer Research, 15, 595-599, 1988.
25. Tracy, D. S. and Osahan, S. S. An improved randomized response technique, Pakistan Jour- nal of Statistics, 15 (1), 1 - 6, 1999.
26. Usman, A., and Oshungade, I. O. A Two-way Randomized Response Technique in Strati- cation for Tracking HIV Seroprevalence, Mathematical Theory and Modeling, 2 (7), 86-97, 2012.
27. Warner, S. L. Randomized response: A Survey Technique for Eliminating Evasive Answer Bias, Journal of the American Statistical Association, 60 (309), 63-69, 1965.