IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i7p1718-d1115222.html
   My bibliography  Save this article

Randomized Response Techniques: A Systematic Review from the Pioneering Work of Warner (1965) to the Present

Author

Listed:
  • Truong-Nhat Le

    (Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam)

  • Shen-Ming Lee

    (Department of Statistics, Feng Chia University, Taichung 40724, Taiwan)

  • Phuoc-Loc Tran

    (Department of Mathematics, College of Natural Science, Can Tho University, Can Tho 900000, Vietnam)

  • Chin-Shang Li

    (School of Nursing, The State University of New York, Buffalo, NY 14214, USA)

Abstract

The randomized response technique is one of the most commonly used indirect questioning methods to collect data on sensitive characteristics in survey research covering a wide variety of statistical applications including, e.g., behavioral science, socio-economic, psychological, epidemiology, biomedical, and public health research disciplines. After nearly six decades since the technique was invented, many improvements of the randomized response techniques have appeared in the literature. This work provides several different aspects of improvements of the original randomized response work of Warner, as well as statistical methods used in the RR problems.

Suggested Citation

  • Truong-Nhat Le & Shen-Ming Lee & Phuoc-Loc Tran & Chin-Shang Li, 2023. "Randomized Response Techniques: A Systematic Review from the Pioneering Work of Warner (1965) to the Present," Mathematics, MDPI, vol. 11(7), pages 1-26, April.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1718-:d:1115222
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/7/1718/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/7/1718/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ghulam Narjis & Javid Shabbir, 2021. "Bayesian analysis of optional unrelated question randomized response models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(18), pages 4203-4215, August.
    2. Shen-Ming Lee & Phuoc-Loc Tran & Truong-Nhat Le & Chin-Shang Li, 2023. "Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    3. Heiko Groenitz, 2018. "Logistic regression analyses for indirect data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(16), pages 3838-3856, August.
    4. Fatima Batool & Javid Shabbir, 2016. "A two-stage design for multivariate estimation of proportions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(18), pages 5412-5426, September.
    5. Pier Francesco Perri & Elvira Pelle & Manuela Stranges, 2016. "Estimating Induced Abortion and Foreign Irregular Presence Using the Randomized Response Crossed Model," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 129(2), pages 601-618, November.
    6. Shu-Hui Hsieh & Shen-Ming Lee & Su-Hao Tu, 2018. "Randomized response techniques for a multi-level attribute using a single sensitive question," Statistical Papers, Springer, vol. 59(1), pages 291-306, March.
    7. Shen-Ming Lee & T. Martin Lukusa & Chin-Shang Li, 2020. "Estimation of a zero-inflated Poisson regression model with missing covariates via nonparametric multiple imputation methods," Computational Statistics, Springer, vol. 35(2), pages 725-754, June.
    8. Pei-Chieh Chang & Kim-Hung Pho & Shen-Ming Lee & Chin-Shang Li, 2021. "Estimation of parameters of logistic regression for two-stage randomized response technique," Computational Statistics, Springer, vol. 36(3), pages 2111-2133, September.
    9. Zofia Mielecka-Kubień & Mariusz Toniszewski, 2022. "Estimation of illicit drug use among high school students in the Silesian voivodship (Poland) with the use of the randomized response technique," Mathematical Population Studies, Taylor & Francis Journals, vol. 29(2), pages 47-57, April.
    10. Burgstaller, Lilith & Feld, Lars P. & Pfeil, Katharina, 2022. "Working in the shadow: Survey techniques for measuring and explaining undeclared work," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 661-671.
    11. Balgobin Nandram & Yuan Yu, 2019. "Bayesian Analysis of Sparse Counts Obtained From the Unrelated Question Design," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(5), pages 66-84, September.
    12. Graeme Blair & Kosuke Imai & Yang-Yang Zhou, 2015. "Design and Analysis of the Randomized Response Technique," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1304-1319, September.
    13. Shen-Ming Lee & Ter-Chao Peng & Jean de Dieu Tapsoba & Shu-Hui Hsieh, 2017. "Improved estimation methods for unrelated question randomized response techniques," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(16), pages 8101-8112, August.
    14. Shu-Hui Hsieh & Shen-Ming Lee & Chin-Shang Li & Su-Hao Tu, 2016. "An alternative to unrelated randomized response techniques with logistic regression analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 601-621, November.
    15. Zawar Hussain & Sidra Shakeel & Salman A. Cheema, 2022. "Estimation of stigmatized population total: A new additive quantitative randomized response model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(24), pages 8741-8753, December.
    16. James Abernathy & Bernard Greenberg & Daniel Horvitz, 1970. "Estimates of induced abortion in urban North Carolina," Demography, Springer;Population Association of America (PAA), vol. 7(1), pages 19-29, February.
    17. Purnima Shaw & Arijit Chaudhuri, 2022. "Further improvements on unrelated characteristic models in randomized response techniques," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(21), pages 7305-7321, November.
    18. Tan, Ming T. & Tian, Guo-Liang & Tang, Man-Lai, 2009. "Sample Surveys With Sensitive Questions: A Nonrandomized Response Approach," The American Statistician, American Statistical Association, vol. 63(1), pages 9-16.
    19. Ivar Krumpal & Thomas Voss, 2020. "Sensitive Questions and Trust: Explaining Respondents’ Behavior in Randomized Response Surveys," SAGE Open, , vol. 10(3), pages 21582440209, July.
    20. Ronning, Gerd, 2005. "Randomized response and the binary probit model," Economics Letters, Elsevier, vol. 86(2), pages 221-228, February.
    21. Shen‐Ming Lee & Truong‐Nhat Le & Phuoc‐Loc Tran & Chin‐Shang Li, 2022. "Investigating the association of a sensitive attribute with a random variable using the Christofides generalised randomised response design and Bayesian methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1471-1502, November.
    22. Arijit Chaudhuri, 2004. "Christofides’ randomized response technique in complex sample surveys," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(3), pages 223-228, November.
    23. Migon, Helio S. & Tachibana, Vilma M., 1997. "Bayesian approximations in randomized response model," Computational Statistics & Data Analysis, Elsevier, vol. 24(4), pages 401-409, June.
    24. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    25. Christopher R. Gjestvang & Sarjinder Singh, 2006. "A new randomized response model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 523-530, June.
    26. Guo-Liang Tian, 2014. "A new non-randomized response model: The parallel model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(4), pages 293-323, November.
    27. Tasos Christofides, 2005. "Randomized response technique for two sensitive characteristics at the same time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 53-63, September.
    28. van den Hout, Ardo & Kooiman, Peter, 2006. "Estimating the linear regression model with categorical covariates subject to randomized response," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3311-3323, July.
    29. Shaul Bar-Lev & Elizabeta Bobovich & Benzion Boukai, 2003. "A common conjugate prior structure for several randomized response models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 101-113, June.
    30. van den Hout, Ardo & van der Heijden, Peter G.M. & Gilchrist, Robert, 2007. "The logistic regression model with response variables subject to randomized response," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6060-6069, August.
    31. Shu-Hui Hsieh & Shen-Ming Lee & Chin-Shang Li, 2022. "A Two-stage Multilevel Randomized Response Technique With Proportional Odds Models and Missing Covariates," Sociological Methods & Research, , vol. 51(1), pages 439-467, February.
    32. Jun-Wu Yu & Guo-Liang Tian & Man-Lai Tang, 2008. "Two new models for survey sampling with sensitive characteristic: design and analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 251-263, April.
    33. Kuo‐Chung Huang, 2004. "A survey technique for estimating the proportion and sensitivity in a dichotomous finite population," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(1), pages 75-82, February.
    34. Heiko Groenitz, 2014. "A new privacy-protecting survey design for multichotomous sensitive variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 211-224, February.
    35. Heiko Groenitz, 2015. "Using prior information in privacy-protecting survey designs for categorical sensitive variables," Statistical Papers, Springer, vol. 56(1), pages 167-189, February.
    36. Hsieh, S.H. & Lee, S.M. & Shen, P.S., 2009. "Semiparametric analysis of randomized response data with missing covariates in logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2673-2692, May.
    37. Gerty J. L. M. Lensvelt‐Mulders & Peter G. M. Van Der Heijden & Olav Laudy & Ger Van Gils, 2006. "A validation of a computer‐assisted randomized response survey to estimate the prevalence of fraud in social security," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 305-318, March.
    38. Shen-Ming Lee & Truong-Nhat Le & Phuoc-Loc Tran & Chin-Shang Li, 2023. "Estimation of logistic regression with covariates missing separately or simultaneously via multiple imputation methods," Computational Statistics, Springer, vol. 38(2), pages 899-934, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shen-Ming Lee & Phuoc-Loc Tran & Truong-Nhat Le & Chin-Shang Li, 2023. "Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    2. Shen‐Ming Lee & Truong‐Nhat Le & Phuoc‐Loc Tran & Chin‐Shang Li, 2022. "Investigating the association of a sensitive attribute with a random variable using the Christofides generalised randomised response design and Bayesian methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1471-1502, November.
    3. Heiko Groenitz, 2015. "Using prior information in privacy-protecting survey designs for categorical sensitive variables," Statistical Papers, Springer, vol. 56(1), pages 167-189, February.
    4. Guo-Liang Tian, 2014. "A new non-randomized response model: The parallel model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(4), pages 293-323, November.
    5. Pei-Chieh Chang & Kim-Hung Pho & Shen-Ming Lee & Chin-Shang Li, 2021. "Estimation of parameters of logistic regression for two-stage randomized response technique," Computational Statistics, Springer, vol. 36(3), pages 2111-2133, September.
    6. Groenitz, Heiko, 2016. "A covariate nonrandomized response model for multicategorical sensitive variables," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 124-138.
    7. Raghunath Arnab & Dahud Kehinde Shangodoyin & Antonio Arcos, 2019. "Nonrandomized Response Model For Complex Survey Designs," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 67-86, March.
    8. Andreas Lagerås & Mathias Lindholm, 2020. "How to ask sensitive multiple‐choice questions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 397-424, June.
    9. Liu, Yin & Tian, Guo-Liang, 2013. "A variant of the parallel model for sample surveys with sensitive characteristics," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 115-135.
    10. Shu-Hui Hsieh & Shen-Ming Lee & Chin-Shang Li, 2022. "A Two-stage Multilevel Randomized Response Technique With Proportional Odds Models and Missing Covariates," Sociological Methods & Research, , vol. 51(1), pages 439-467, February.
    11. María del Mar Rueda & Beatriz Cobo & Antonio Arcos, 2021. "Regression Models in Complex Survey Sampling for Sensitive Quantitative Variables," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
    12. Lucio Barabesi & Marzia Marcheselli, 2010. "Bayesian estimation of proportion and sensitivity level in randomized response procedures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 75-88, July.
    13. Balgobin Nandram & Yuan Yu, 2019. "Bayesian Analysis of Sparse Counts Obtained From the Unrelated Question Design," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(5), pages 66-84, September.
    14. Arnab Raghunath & Shangodoyin Dahud Kehinde & Arcos Antonio, 2019. "Nonrandomized Response Model For Complex Survey Designs," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 67-86, March.
    15. Asma Halim & Irshad Ahmad Arshad & Summaira Haroon & Waqas Shair, 2022. "A Comparative Study of Modified Hidden Logits Using Randomized Response Techniques," Journal of Policy Research (JPR), Research Foundation for Humanity (RFH), vol. 8(4), pages 447-461, December.
    16. Shu-Hui Hsieh & Shen-Ming Lee & Chin-Shang Li & Su-Hao Tu, 2016. "An alternative to unrelated randomized response techniques with logistic regression analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 601-621, November.
    17. Burgstaller, Lilith & Feld, Lars P. & Pfeil, Katharina, 2022. "Working in the shadow: Survey techniques for measuring and explaining undeclared work," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 661-671.
    18. Hua Xin & Jianping Zhu & Tzong-Ru Tsai & Chieh-Yi Hung, 2021. "Hierarchical Bayesian Modeling and Randomized Response Method for Inferring the Sensitive-Nature Proportion," Mathematics, MDPI, vol. 9(19), pages 1-12, October.
    19. Giancarlo Diana & Pier Francesco Perri, 2010. "New scrambled response models for estimating the mean of a sensitive quantitative character," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(11), pages 1875-1890.
    20. Marc Höglinger & Ben Jann, 2018. "More is not always better: An experimental individual-level validation of the randomized response technique and the crosswise model," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-22, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1718-:d:1115222. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.