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

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.

Automated summary

This study proposes a new three-statement randomized response estimation method to improve the estimation of sensitive-nature proportion (SNP) using hierarchical Bayesian modeling, Gibbs sampling, and Metropolis-Hastings algorithms. Monte Carlo simulations demonstrate that the method is effective and easy to use.