An Analysis of the Properties of a Newly Proposed Non‑Randomised Response Technique
Keywords:indirect questioning, sensitive questions, non‑randomised response techniques, crosswise model, ML estimation, degree of privacy protection
Non‑randomised response (NRR) techniques are modern and constantly evolving methods intended for dealing with sensitive topics in surveys, such as tax evasion, black market, corruption etc. The paper introduces a new NRR technique that can be seen as a generalisation of the well‑known crosswise model (CM). In the paper, methodology of the new generalised crosswise model (GCM) is presented and the maximum likelihood estimator of the unknown population sensitive proportion is obtained. Also, the problem of privacy protection is discussed. The properties of the newly proposed GCM are examined. Then the GCM is compared with the traditional CM. The paper shows that mathematically the CM is a special case of the newly proposed generalised CM and that this generalisation has high practical relevance.
Abdelfatah S., Mazloum R. (2015), Efficient estimation in a two‑stage randomized response model, “Mathematical Population Studies”, vol. 22, pp. 234–251.
Google Scholar DOI: https://doi.org/10.1080/08898480.2014.953897
Arnab R., Shangodoyin D. K., Arcos A. (2019), Nonrandomized Response model for Complex Survey Designs, “Statistics in Transition New Series”, vol. 20, pp. 67–86.
Google Scholar DOI: https://doi.org/10.21307/stattrans-2019-004
Batool F., Shabbir J., Hussain Z. (2017), An improved binary randomized response model using six decks of cards, “Communications in Statistics – Simulation and Computation”, vol. 46, pp. 2548–2562.
Google Scholar DOI: https://doi.org/10.1080/03610918.2015.1053922
Blair G., Imai K., Zhou Y.‑Y. (2015), Design and Analysis of the Randomized Response Technique, “Journal of the American Statistical Association”, vol. 110, pp. 1304–1319.
Google Scholar DOI: https://doi.org/10.1080/01621459.2015.1050028
Boruch R. F. (1971), Assuring Confidentiality of Responses in Social Research: A Note on Strategies, “American Sociologist”, vol. 6, pp. 308–311.
Chong A. C.Y., Chu A. M.Y, So M. K.P, Chung R. S.W. (2019), Asking Sensitive Questions Using the Randomized Response Approach in Public Health Research: An Empirical Study on the Factors of Illegal Waste Disposal, “International Journal of Environmental Research and Public Health”, vol. 16(6), https://www.researchgate.net/publication/331848508_Asking_Sensitive_Questions_Using_the_Randomized_Response_Approach_in_Public_Health_Research_An_Empirical_Study_on_the_Factors_of_Illegal_Waste_Disposal (accessed: 4.01.2022).
Google Scholar DOI: https://doi.org/10.3390/ijerph16060970
Chu A. M.Y., So M. K.P., Chung R. S.W. (2018), Applying the Randomized Response Technique in Business Ethics Research: The Misuse of Information Systems Resources in the Workplace, “Journal of Business Ethics”, vol. 151, pp. 195–212.
Google Scholar DOI: https://doi.org/10.1007/s10551-016-3240-5
Coutts E., Jann B. (2011), Sensitive questions in online surveys: Experimental results for the randomized response technique (RRT) and the unmatched count technique (UCT), “Sociological Methods & Research”, vol. 40, pp. 169–193.
Google Scholar DOI: https://doi.org/10.1177/0049124110390768
Erdmann A. (2019), Non‑Randomized Response Models: An Experimental Application of the Triangular Model as an Indirect Questioning Method for Sensitive Topics, “Methods, Data, Analyses”, vol. 13, pp. 139–167.
Fox J. A., Tracy P. E. (1986), Randomised Response: A Method for Sensitive Surveys, Sage Publications, Beverly Hills.
Gingerich D. W. (2010), Understanding Off‑The‑Books Politics: Conducting Inference on the Determinants of Sensitive Behavior with Randomized Response Surveys, “Political Analysis”, vol. 18, pp. 349–380.
Google Scholar DOI: https://doi.org/10.1093/pan/mpq010
Greenberg B. G., Abul‑Ela A.‑L. A., Horvitz D. G. (1969), The Unrelated Question Randomized Response Model: Theoretical Framework, “Journal of the American Statistical Association”, vol. 64, pp. 520–539.
Google Scholar DOI: https://doi.org/10.1080/01621459.1969.10500991
Hoffmann A., Musch J. (2019), Prejudice against women leaders: Insights from an indirect questioning approach, “Sex Roles”, vol. 80, pp. 681–692.
Google Scholar DOI: https://doi.org/10.1007/s11199-018-0969-6
Hoffmann A., Meisters J., Musch J. (2020), On the validity of non‑randomized response techniques: an experimental comparison of the crosswise model and the triangular model, “Behavior Research”, vol. 52, pp. 1768–1782.
Google Scholar DOI: https://doi.org/10.3758/s13428-020-01349-9
Johann D., Thomas K. (2017), Testing the Validity of the Crosswise Model: A Study on Attitudes Towards Muslims Survey Methods: Insights from the Field, https://surveyinsights.org/?p=8887 (accessed: 4.01.2022).
Khalil S., Zhang Q., Gupta S. (2021), Mean estimation of sensitive variables under measurement errors using optional RRT models, “Communications in Statistics – Simulation and Computation”, vol. 50, pp. 1417–1426.
Google Scholar DOI: https://doi.org/10.1080/03610918.2019.1584298
Korndörfer M., Krumpal I., Schmukle S. C. (2014), Measuring and explaining tax evasion: Improving self‑reports using the crosswise model, “Journal of Economic Psychology”, vol. 45, pp. 18–32.
Google Scholar DOI: https://doi.org/10.1016/j.joep.2014.08.001
Leslie K. J., Loewenstein G. F., Acquisti A., Vosgerau J. (2018), When and Why Randomized Response Techniques (Fail To) Elicit the Truth, “Organizational Behavior and Human Decision Processes”, vol. 148(C), pp. 101–123.
Google Scholar DOI: https://doi.org/10.1016/j.obhdp.2018.07.004
Rueda M. M., Cobo B., López‑Torrecillas F. (2020), Measuring Inappropriate Sexual Behavior Among University Students: Using the Randomized Response Technique to Enhance Self‑Reporting, “Sex Abuse”, vol. 32, pp. 320–334.
Google Scholar DOI: https://doi.org/10.1177/1079063219825872
Vishwakarma G. K., Singh N. (2021), Computing the effect of measurement errors under additive scramble response of the sensitive variable, “Journal of Computational and Applied Mathematics”, vol. 395, 113593.
Google Scholar DOI: https://doi.org/10.1016/j.cam.2021.113593
Warner S. L. (1965), Randomized Response: A Survey Technique for Eliminating Evasive Answer Bias, “Journal of the American Statistical Association”, vol. 60, pp. 63–69.
Google Scholar DOI: https://doi.org/10.1080/01621459.1965.10480775
Wolter F., Preisendörfer P. (2013), Asking sensitive questions: An evaluation of the randomized response technique versus direct questioning using individual validation data, “Sociological Methods & Research”, vol. 42, pp. 321–353.
Google Scholar DOI: https://doi.org/10.1177/0049124113500474
Wu Q., Tang M. L. (2016), Non‑randomized response model for sensitive survey with noncompliance, “Statistical Methods in Medical Research”, vol. 25, pp. 2827–2839.
Google Scholar DOI: https://doi.org/10.1177/0962280214533022
Yu J. W., Tian G. L., Tang M. L. (2008), Two new models for survey sampling with sensitive characteristic: Design and analysis, “Metrika”, vol. 67, pp. 251–263.
Google Scholar DOI: https://doi.org/10.1007/s00184-007-0131-x
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