IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v25y2016i4d10.1007_s10260-016-0351-1.html
   My bibliography  Save this article

An alternative to unrelated randomized response techniques with logistic regression analysis

Author

Listed:
  • Shu-Hui Hsieh

    (Academia Sinica)

  • Shen-Ming Lee

    (Feng Chia University)

  • Chin-Shang Li

    (University of California)

  • Su-Hao Tu

    (Academia Sinica)

Abstract

The randomized response technique (RRT) is an important tool that is commonly used to protect a respondent’s privacy and avoid biased answers in surveys on sensitive issues. In this work, we consider the joint use of the unrelated-question RRT of Greenberg et al. (J Am Stat Assoc 64:520–539, 1969) and the related-question RRT of Warner (J Am Stat Assoc 60:63–69, 1965) dealing with the issue of an innocuous question from the unrelated-question RRT. Unlike the existing unrelated-question RRT of Greenberg et al. (1969), the approach can provide more information on the innocuous question by using the related-question RRT of Warner (1965) to effectively improve the efficiency of the maximum likelihood estimator of Scheers and Dayton (J Am Stat Assoc 83:969–974, 1988). We can then estimate the prevalence of the sensitive characteristic by using logistic regression. In this new design, we propose the transformation method and provide large-sample properties. From the case of two survey studies, an extramarital relationship study and a cable TV study, we develop the joint conditional likelihood method. As part of this research, we conduct a simulation study of the relative efficiencies of the proposed methods. Furthermore, we use the two survey studies to compare the analysis results under different scenarios.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:25:y:2016:i:4:d:10.1007_s10260-016-0351-1
    DOI: 10.1007/s10260-016-0351-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-016-0351-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-016-0351-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shen-Ming Lee & Chin-Shang Li & Shu-Hui Hsieh & Li-Hui Huang, 2012. "Semiparametric estimation of logistic regression model with missing covariates and outcome," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 621-653, July.
    2. Gerty J. L. M. Lensvelt-Mulders & Joop J. Hox & Peter G. M. van der Heijden & Cora J. M. Maas, 2005. "Meta-Analysis of Randomized Response Research," Sociological Methods & Research, , vol. 33(3), pages 319-348, February.
    3. 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.
    4. 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.
    5. 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.
    6. Hsieh, Shu-Hui & Li, Chin-Shang & Lee, Shen-Ming, 2013. "Logistic regression with outcome and covariates missing separately or simultaneously," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 32-54.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    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. Kim-Hung Pho & Michael McAleer, 2021. "Specification and Estimation of a Logistic Function, with Applications in the Sciences and Social Sciences," Advances in Decision Sciences, Asia University, Taiwan, vol. 25(2), pages 74-104, June.
    2. 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.
    3. 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.
    4. Kim-Hung Pho & Tuan-Kiet Tran & Thi Diem-Chinh Ho & Wing-Keung Wong, 2019. "Optimal Solution Techniques in Decision Sciences A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 114-161, March.
    5. 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.
    6. Antonio Arcos & María del Rueda & Sarjinder Singh, 2015. "A generalized approach to randomised response for quantitative variables," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 1239-1256, May.
    7. Buu-Chau Truong & Nguyen Van Thuan & Nguyen Huu Hau & Michael McAleer, 2019. "Applications of the Newton-Raphson Method in Decision Sciences and Education," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(4), pages 52-80, December.
    8. 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.
    9. T. Martin Lukusa & Shen-Ming Lee & Chin-Shang Li, 2016. "Semiparametric estimation of a zero-inflated Poisson regression model with missing covariates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(4), pages 457-483, May.
    10. 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.
    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. 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.
    13. Housila P. Singh & Swarangi M. Gorey, 2017. "A Generalized Randomized Response Model," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 669-686, December.
    14. Blume, Andreas & Lai, Ernest K. & Lim, Wooyoung, 2019. "Eliciting private information with noise: The case of randomized response," Games and Economic Behavior, Elsevier, vol. 113(C), pages 356-380.
    15. Isabel Thielmann & Daniel W. Heck & Benjamin E. Hilbig, 2016. "Anonymity and incentives: An investigation of techniques to reduce socially desirable responding in the Trust Game," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 11(5), pages 527-536, September.
    16. John, Leslie K. & Loewenstein, George & Acquisti, Alessandro & Vosgerau, Joachim, 2018. "When and why randomized response techniques (fail to) elicit the truth," Organizational Behavior and Human Decision Processes, Elsevier, vol. 148(C), pages 101-123.
    17. Erum Zahid & Javid Shabbir & Sat Gupta & Ronald Onyango & Sadia Saeed, 2022. "A generalized class of estimators for sensitive variable in the presence of measurement error and non-response," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-19, January.
    18. Bernard GAUTHIER & Frédéric LESNÉ, 2017. "Measuring corruption in presence of reticent respondents: Theory and Application," Working Papers P207, FERDI.
    19. Dihidar Kajal & Bhattacharya Manjima, 2017. "Estimating Sensitive Population Proportion Using a Combination of Binomial and Hypergeometric Randomized Responses by Direct and Inverse Mechanism," Statistics in Transition New Series, Polish Statistical Association, vol. 18(2), pages 193-210, June.
    20. 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.

    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:spr:stmapp:v:25:y:2016:i:4:d:10.1007_s10260-016-0351-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.