IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i19p2518-d651317.html
   My bibliography  Save this article

Hierarchical Bayesian Modeling and Randomized Response Method for Inferring the Sensitive-Nature Proportion

Author

Listed:
  • Hua Xin

    (School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China
    These authors contributed equally to this work.)

  • Jianping Zhu

    (School of Management and Data-Mining Research Center, Xiamen University, Xiamen 361005, China
    These authors contributed equally to this work.)

  • Tzong-Ru Tsai

    (Department of Statistics, Tamkang University, New Taipei City 251301, Taiwan
    These authors contributed equally to this work.)

  • Chieh-Yi Hung

    (Department of Statistics, Tamkang University, New Taipei City 251301, Taiwan
    These authors contributed equally to this work.)

Abstract

In this study, a new three-statement randomized response estimation method is proposed to improve the drawback that the maximum likelihood estimation method could generate a negative value to estimate the sensitive-nature proportion (SNP) when its true value is small. The Bayes estimator of the SNP is obtained via using a hierarchical Bayesian modeling procedure. Moreover, a hybrid algorithm using Gibbs sampling in Metropolis–Hastings algorithms is used to obtain the Bayes estimator of the SNP. The highest posterior density interval of the SNP is obtained based on the empirical distribution of Markov chains. We use the term 3RR-HB to denote the proposed method here. Monte Carlo simulations show that the quality of 3RR-HB procedure is good and that it can improve the drawback of the maximum likelihood estimation method. The proposed 3RR-HB procedure is simple for use. An example regarding the homosexual proportion of college freshmen is used for illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2518-:d:651317
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/19/2518/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/19/2518/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    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. 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.
    2. Lucio Barabesi & Giancarlo Diana & Pier Perri, 2013. "Design-based distribution function estimation for stigmatized populations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 919-935, October.
    3. 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.
    4. 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.
    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. Lucio Barabesi & Sara Franceschi & Marzia Marcheselli, 2012. "A randomized response procedure for multiple-sensitive questions," Statistical Papers, Springer, vol. 53(3), pages 703-718, August.
    7. 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.
    8. 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.
    9. Lucio Barabesi & Giancarlo Diana & Pier Perri, 2015. "Gini index estimation in randomized response surveys," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 45-62, 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:gam:jmathe:v:9:y:2021:i:19:p:2518-:d:651317. 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.