Survey Methodology
Bayesian predictive inference of a proportion under a two‑fold small area model with heterogeneous correlations

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by Danhyang Lee, Balgobin Nandram and Dalho KimNote 1

  • Release date: June 22, 2017
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Abstract

We use a Bayesian method to infer about a finite population proportion when binary data are collected using a two-fold sample design from small areas. The two-fold sample design has a two-stage cluster sample design within each area. A former hierarchical Bayesian model assumes that for each area the first stage binary responses are independent Bernoulli distributions, and the probabilities have beta distributions which are parameterized by a mean and a correlation coefficient. The means vary with areas but the correlation is the same over areas. However, to gain some flexibility we have now extended this model to accommodate different correlations. The means and the correlations have independent beta distributions. We call the former model a homogeneous model and the new model a heterogeneous model. All hyperparameters have proper noninformative priors. An additional complexity is that some of the parameters are weakly identified making it difficult to use a standard Gibbs sampler for computation. So we have used unimodal constraints for the beta prior distributions and a blocked Gibbs sampler to perform the computation. We have compared the heterogeneous and homogeneous models using an illustrative example and simulation study. As expected, the two-fold model with heterogeneous correlations is preferred.

Key Words: Blocked Gibbs sampler; Hierarchical Bayesian model; Intracluster and intercluster correlations; Goodness of fit; Unimodality; Weakly identifiable.

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How to cite

Lee, D., Nandram, B. and Kim, D. (2017). Bayesian predictive inference of a proportion under a two‑fold small area model with heterogeneous correlations. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 43, No. 1. Paper available at http://www.statcan.gc.ca/pub/12‑001‑x/2017001/article/14822-eng.htm.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Published by authority of the Minister responsible for Statistics Canada.

© Minister of Industry, 2017

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Bayesian two-fold small area models and computations
Section 3. Numerical study and comparisons
Section 4. Concluding remarks
Acknowledgements
Appendix A
Appendix B
References

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