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Hierarchical Bayesian pattern mixture models for binary data from small area
Journal of the Korean Data & Information Science Society 2019;30:1409-21
Published online November 30, 2019;
© 2019 Korean Data and Information Science Society.

Sukyoung An1 · 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:
Received September 1, 2019; Revised September 11, 2019; Accepted September 11, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
The purpose of many surveys is to estimate the probability of a group having certain characteristics. However, if the survey has a lot of missing data, we may get incorrect results. So a lot of research has been done on missing data since the past. There are many methods to handle missing data, so it is better to use various methods than one. We estimate the proportion of finite population using the Bayesian method using the pattern mixture model for binary data. We consider a hierarchical Bayesian model to increase the reliability of small data. We have applied various cases on the hyperparameter of the prior distribution of proportion for nonresponse to confirm that the proportion estimate is not sensitive. We also confirmed that small area estimation is better than the individual area estimation.
Keywords : Gibbs sampler, hierarchical Bayesian model, pattern mixture approach, small area estimation.