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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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)

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