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

Hua Xin, Jianping Zhu, Tzong-Ru Tsai and Chieh-Yi Hung
Additional contact information
Hua Xin: School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China
Jianping Zhu: School of Management and Data-Mining Research Center, Xiamen University, Xiamen 361005, China
Tzong-Ru Tsai: Department of Statistics, Tamkang University, New Taipei City 251301, Taiwan
Chieh-Yi Hung: Department of Statistics, Tamkang University, New Taipei City 251301, Taiwan

Mathematics, 2021, vol. 9, issue 19, 1-12

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.

Keywords: Bayesian estimation; Beta-Binominal model; maximum likelihood estimation; respondent protection; randomized response (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/19/2518/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/19/2518/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:19:p:2518-:d:651317

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().