Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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A Bayesian model for two-way contingency tables with nonignorable nonresponse from small areas

  • Woo, Namkyo (Department of Statistics, Kyungpook National University) ;
  • Kim, Dal Ho (Department of Statistics, Kyungpook National University)
  • Received : 2015.09.28
  • Accepted : 2015.11.25
  • Published : 2016.01.31
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Abstract

Many surveys provide categorical data and there may be one or more missing categories. We describe a nonignorable nonresponse model for the analysis of two-way contingency tables from small areas. There are both item and unit nonresponse. One approach to analyze these data is to construct several tables corresponding to missing categories. We describe a hierarchical Bayesian model to analyze two-way categorical data from different areas. This allows a "borrowing of strength" of the data from larger areas to improve the reliability in the estimates of the model parameters corresponding to the small areas. Also we use a nonignorable nonresponse model with Bayesian uncertainty analysis by placing priors in nonidentifiable parameters instead of a sensitivity analysis for nonidentifiable parameters. We use the griddy Gibbs sampler to fit our models and compute DIC and BPP for model diagnostics. We illustrate our method using data from NHANES III data on thirteen states to obtain the finite population proportions.

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References

  1. Choi, S. M. and Kim, D. H. (2013). Bayesian estimation for nite population proportion under selection bias via surrogate samples. Journal of the Korean Data & Information Science Society, 24, 1543-1550. https://doi.org/10.7465/jkdi.2013.24.6.1543
  2. Choi, S. M. and Kim, D. H. (2014). Sensitivity analysis in Bayesian nonignorable selection model for binary responses. Journal of the Korean Data & Information Science Society, 25, 187-194. https://doi.org/10.7465/jkdi.2014.25.1.187
  3. Greenland, S. (2009). Relaxation penalties and priors for plausible modeling of nonidenti ed bias sources, Statistical Sciences, 24, 195-210. https://doi.org/10.1214/09-STS291
  4. Little, R. J. A. and Rubin D. B. (2002). Statistical analysis with missing data. Wiley, New York.
  5. Molenberghs, G., Kenward, M. G. and Goetghebeur, E. (2001). Sensitivity analysis for incomplete contingency table: The Slovenian plebiscite case. Journal of the American Statistical Association, 97, 381-388.
  6. Nandram, B. and Choi, J. W. (2005). Hierarchical Bayesian nonignorable nonresponse regression models for small areas: An application to the NHANES data. Survey Methodology, 31, 73-84.
  7. Nandram, B. and Choi, J. W. (2008). A Bayesian allocation of undecided voters. Survey Methodology, 34, 37-49.
  8. Nandram, B. and Choi, J. W. (2010). A Bayesian analysis of body mass index data from small domains under nonignorable nonresponse and selection. Journal of the American Statistical Association, 105, 120-135. https://doi.org/10.1198/jasa.2009.ap08443
  9. National Center for Health Statistics. (1992). Third national health and nutrition examination survey. Vital and Health Statistics Series 2, 113.
  10. Rubin, D. B., Stern, H. S. and Behovar, V. (1995). Handling "Don't Know" survey responses: The case of the Slovenian plebiscite. Journal of the American Statistical Association, 72, 822-828.
  11. Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581-592. https://doi.org/10.1093/biomet/63.3.581
  12. Yan, G. and Sedransk, J. (2007). Bayesian diagnostic techniques for detecting hierarchical structure. Bayesian Analysis, 2, 735-760. https://doi.org/10.1214/07-BA230

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