Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Bayesian pooling for contingency tables from small areas

  • Jo, Aejung (Department of Statistics, Kyungpook National University) ;
  • Kim, Dal Ho (Department of Statistics, Kyungpook National University)
  • Received : 2016.09.18
  • Accepted : 2016.10.24
  • Published : 2016.11.30
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Abstract

This paper studies Bayesian pooling for analysis of categorical data from small areas. Many surveys consist of categorical data collected on a contingency table in each area. Statistical inference for small areas requires considerable care because the subpopulation sample sizes are usually very small. Typically we use the hierarchical Bayesian model for pooling subpopulation data. However, the customary hierarchical Bayesian models may specify more exchangeability than warranted. We, therefore, investigate the effects of pooling in hierarchical Bayesian modeling for the contingency table from small areas. In specific, this paper focuses on the methods of direct or indirect pooling of categorical data collected on a contingency table in each area through Dirichlet priors. We compare the pooling effects of hierarchical Bayesian models by fitting the simulated data. The analysis is carried out using Markov chain Monte Carlo methods.

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References

  1. Dunson, D. B. (2009). Nonparametric Bayes local partition models for random effects. Biometrika, 96, 249-262. https://doi.org/10.1093/biomet/asp021
  2. Evans, R. and Sedransk, J. (1999). Methodoloty for pooling subpopulation regressions when sample sizes are small and there is uncertainty about which subpopulations are similar. Statistica Sinica, 9, 345-359.
  3. Evans, R. and Sedransk, J. (2003). Bayesian methodology for combining the results from different experiments when the specifications for pooling are uncertain: II. Journal of Statiatical Planning and Inference, 111, 95-100. https://doi.org/10.1016/S0378-3758(02)00287-2
  4. Gneiting, T. and Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association, 102, 359-378. https://doi.org/10.1198/016214506000001437
  5. Malec, D. and Sedransk, J. (1992). Bayesian methodology for combining the results from different experiments when the specifications for pooling are uncertain. Biometrika, 79, 593-601. https://doi.org/10.1093/biomet/79.3.593
  6. Woo, N. and Kim, D. H. (2015). A Bayesian uncertainty analysis for nonignorable nonresponse in two-way contingency table. Journal of the Korean Data & Information Science Society, 26, 1547-1555. https://doi.org/10.7465/jkdi.2015.26.6.1547
  7. Woo, N. and Kim, D. H. (2016). A Bayesian model for two-way contingency tables with nonignorable nonresponse from small areas. Journal of the Korean Data & Information Science Society, 27, 245-254. https://doi.org/10.7465/jkdi.2016.27.1.245