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Bayesian analysis of a sensitive proportion for a small area
Journal of the Korean Data & Information Science Society 2019;30:1423-30
Published online November 30, 2019;  https://doi.org/10.7465/jkdi.2019.30.6.1423
© 2019 Korean Data and Information Science Society.

WonYoung Yun1 · Balgobin Nandram2 · Dal Ho Kim3

13Department of Statistics, Kyungpook National University
2Department of Mathematical Sciences, Worcester Polytechnic Institute
Correspondence to: Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail: dalkim@knu.ac.kr
Received September 1, 2019; Revised September 17, 2019; Accepted September 17, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
When respondents are asked to answer sensitive questions, they are more likely to response untruthfully as they hesitate to expose their identity. Warner (1965) proposed a randomized design that uses a randomization device that is designed to conceal individual response and protect the respondent privacy, to reduce the response bias that can be generated through this. After that, numerous survey designs to reduce the response bias were proposed, and various estimation and simulation methods were studied from the Bayesian perspective. This study proposes an analysis method that has taken account of small-area to minimize the posterior standard deviation of sensitive proportions in a survey with sensitive questions. Then it compares the results between the individual model and the small-area model through the simulation. In addition, this study applies the two models which has and has not considered the small-area to the actual survey with sensitive questionnaires related to the organizational commitment to the experienced employees. This study confirms the results based on real data.
Keywords : Blocked Gibbs sampler, latent variables, mirrored question design.