Enhancing the efficiency of randomized response techniques using direct responses
Main Article Content
Abstract
The quality of the findings of a research study largely depends on data it is based on. Many research studies require data collection from a sample of human participants. Respondents’ refusals and untruthful responses are common issues in surveys based on human participants. Randomized response survey methods ensure the respondents’ privacy protection, motivating them for participation in the survey. The existing scrambling methods do not offer the respondents to report the direct response. In practice, survey statisticians face situations where some of the survey participants may be willing to report their direct responses, thus avoiding the complex process of scrambling the responses. Moreover, some recent models involve a complicated scrambling process which may put a burden on the respondents which makes it difficult to practically implement such models in sample surveys. We propose two novel randomized response techniques using both the direct and scrambling response options. The proposed techniques are found to achieve a significant boost in efficiency over the competitor techniques. The efficiency conditions have been derived and are found mathematically strong. The results suggest that the proposed techniques are suitable for implementation in practical sample surveys.
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References
1. Abbasi, A.M., & Asghar, A. An improved quantitative randomized response model under ranked set sampling. Pakistan Journal of Statistics 40, 225-242 (2024).
2. Abbasi, A.M., Shad, M.Y., & Ahmad, A. On partial randomized response model using ranked set sampling. PLOS ONE 17, e0277497. https://doi.org/10.1371/journal.pone.0277497
3. Azeem, M., & Ali, S. A neutral comparative analysis of additive, multiplicative, and mixed quantitative randomized response models. PLOS ONE 18, e0284995 (2023). https://doi.org/10.1371/journal.pone.0284995
4. Azeem, M. Incorporating direct responses into optional randomized response models without compromising respondents’ privacy: Accepted-March 2024. REVSTAT – Statistical Journal (2024). https://revstat.ine.pt/index.php/REVSTAT/article/view/663
5. Azeem, M. Introducing a weighted measure of privacy and efficiency for comparison of quantitative randomized response models. Pakistan Journal of Statistics 39, 377-385 (2023).
6. Bar-Lev, S. K., Bobovitch, E., & Boukai, B. A note on randomized response models for quantitative data. Metrika 60, 255-260 (2004). https://doi.org/10.1007/s001840300308
7. Bouza-Herrera, C. N. Behavior of some scrambled randomized response models under simple random sampling, ranked set sampling and Rao–Hartley–Cochran designs. In Handbook of Statistics 34, 209-220 (2016). https://doi.org/10.1016/bs.host.2016.01.011
8. Eichhorn, B. H., & Hayre, L. S. Scrambled randomized response methods for obtaining sensitive quantitative data. Journal of Statistical Planning and Inference 7, 307-316 (1983). https://doi.org/10.1016/0378-3758(83)90002-2
9. Franklin, L. R. A. A comparison of estimators for randomized response sampling with continuous distributions from a dichotomous population. Communications in Statistics-Theory and Methods 18, 489-505 (1989). https://doi.org/10.1080/03610928908829913
10. Gupta, S., Gupta, B., & Singh, S. Estimation of sensitivity level of personal interview survey questions. Journal of Statistical Planning and Inference 100, 239-247 (2002). https://doi.org/10.1016/S0378-3758(01)00137-9
11. Gjestvang, C. R., & Singh, S. An improved randomized response model: Estimation of mean. Journal of Applied Statistics 36, 1361-1367 (2009).https://doi.org/10.1080/02664760802684151
12. Gupta, S., Mehta, S., Shabbir, J., & Khalil, S. A unified measure of respondent privacy and model efficiency in quantitative RRT models. Journal of Statistical Theory and Practice 12, 506-511 (2018). https://doi.org/10.1080/15598608.2017.1415175
13. Gupta, S., Zhang, J., Khalil, S., & Sapra, P. Mitigating lack of trust in quantitative randomized response technique models. Communications in Statistics - Simulation and Computation 53, 2624-2632 (2024). https://doi.org/10.1080/03610918.2022.2082477
14. Himmelfarb, S., & Edgell, S. E. Additive constants model: A randomized response technique for eliminating evasiveness to quantitative response questions. Psychological Bulletin 87, 525 (1980). https://doi.org/10.1037/0033-2909.87.3.525
15. Hussain, Z., Al-Sobhi, M. M., Al-Zahrani, B., Singh, H. P., & Tarray, T. A. Improved randomized response in additive scrambling models. Mathematical Population Studies 23, 205-221 (2016). https://doi.org/10.1080/08898480.2015.1087773
16. Kumar, S., & Kour, S. P. The joint influence of estimation of sensitive variable under measurement error and non-response using ORRT models. Journal of Statistical Computation and Simulation 92, 3583-3604 (2022). https://doi.org/10.1080/00949655.2022.2075362
17. Kumar, S., Kour, S. P., & Singh, H. P. Applying ORRT for the estimation of population variance of sensitive variable. Communications in Statistics-Simulation and Computation 1-11 (2023). https://doi.org/10.1080/03610918.2023.2292966
18. Lovig, M., Khalil, S., Rahman, S., Sapra, P., & Gupta, S. A mixture binary RRT model with a unified measure of privacy and efficiency. Communications in statistics-simulation and computation 52, 2727-2737 (2023). https://doi.org/10.1080/03610918.2021.1914092
19. Mahzizadeh, M., & Zamanzade, E. On estimating the area under ROC curve in ranked set sampling. Statistical Methods in Medical Research 31, 1500-1514 (2022). https://doi.org/10.1177/09622802221097211
20. Mangat, N. S., & Singh, R. An alternative randomized response procedure. Biometrika 77, 439-442 (1990). https://doi.org/10.1093/biomet/77.2.439
21. Mehta, S., & Aggarwal, P. Bayesian estimation of sensitivity level and population proportion of a sensitive characteristic in a binary optional unrelated question RRT model. Communications in Statistics-Theory and Methods 47, 4021-4028 (2018). https://doi.org/10.1080/03610926.2017.1367812
22. Murtaza, M., Singh, S., & Hussain, Z. An innovative optimal randomized response model using correlated scrambling variables. Journal of Statistical Computation and Simulation 90, 2823-2839 (2020). https://doi.org/10.1080/00949655.2020.1791118
23. Narjis, G., & Shabbir, J. An efficient new scrambled response model for estimating sensitive population mean in successive sampling. Communications in Statistics-Simulation and Computation 52, 5327-5344 (2023). https://doi.org/10.1080/03610918.2021.1986528
24. Pollock, K. H., & Bek, Y. A comparison of three randomized response models for quantitative data. Journal of the American Statistical Association 71, 884-886 (1976). https://www.tandfonline.com/doi/abs/10.1080/01621459.1976.10480963
25. Santiago, A., Sautto, J.M., & Bouza, C.N. Randomized estimation a proportion using ranked set sampling and Warner’s procedure. Investigacion Operacional 40, 356-361 (2019). http://dx.doi.org/10.13140/RG.2.2.11102.95043
26. Singh, S., & Grewal, I. S. Geometric distribution as a randomization device: implemented to the Kuk’s model. International Journal of Contemporary Mathematical Sciences 8, 243-248 (2013).
27. Singh, S., & Sedory, S. A. A new randomized response device for sensitive characteristics: an application of the negative hypergeometric distribution. Metron 71, 3-8 (2013). https://doi.org/10.1007/s40300-013-0002-3
28. Sanaullah, A., Saleem, I., Gupta, S., & Hanif, M. Mean estimation with generalized scrambling using two-phase sampling. Communications in Statistics – Simulation and Computation 51, 5643-5657 (2022). https://doi.org/10.1080/03610918.2020.1778032
29. Tarray, T. A., & Singh, H. P. A general procedure for estimating the mean of a sensitive variable using auxiliary information. Investigación Operacional 36 (2015). https://revistas.uh.cu/invoperacional/article/view/4612
30. Tiwari, N., & Mehta, P. Additive randomized response model with known sensitivity level. International Journal of Computational and Theoretical Statistics 4, 83-93 (2017). http://dx.doi.org/10.12785/IJCTS/040201
31. Warner, S. L. Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association 60, 63-69 (1965). https://doi.org/10.1080/01621459.1965.10480775
32. Yan, Z., Wang, J., & Lai, J. An efficiency and protection degree-based comparison among the quantitative randomized response strategies. Communications in Statistics – Theory and Methods 38, 400-408 (2008). https://doi.org/10.1080/03610920802220785
33. Zamanzade, E., & Wang, X. Proportion estimation in ranked set sampling in the presence of tie information. Computational Statistics 33, 1349-1366 (2018). https://doi.org/10.1007/s00180-018-0807-x