DOI QR코드

DOI QR Code

Bayes tests of independence for contingency tables from small areas

  • Jo, Aejung (Department of Statistics, Kyungpook National University) ;
  • Kim, Dal Ho (Department of Statistics, Kyungpook National University)
  • Received : 2016.10.09
  • Accepted : 2016.11.01
  • Published : 2017.01.31

Abstract

In this paper we study pooling effects in Bayesian testing procedures of independence for contingency tables from small areas. In small area estimation setup, we typically use a hierarchical Bayesian model for borrowing strength across small areas. This techniques of borrowing strength in small area estimation is used to construct a Bayes test of independence for contingency tables from small areas. In specific, we consider the methods of direct or indirect pooling in multinomial models through Dirichlet priors. We use the Bayes factor (or equivalently the ratio of the marginal likelihoods) to construct the Bayes test, and the marginal density is obtained by integrating the joint density function over all parameters. The Bayes test is computed by performing a Monte Carlo integration based on the method proposed by Nandram and Kim (2002).

Keywords

References

  1. Agresti, A. and Hitchcock, D. B. (2005). Bayesian inference for categorical data analysis. Statistical Methods and Applications, 14, 297-330. https://doi.org/10.1007/s10260-005-0121-y
  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 ex-periments 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. Kass, R. E. and Raftery, A. E. (1995). Bayes factor. Journal of the American Statistical Association, 90, 773-795. https://doi.org/10.1080/01621459.1995.10476572
  5. Leonard, T. (1977). Bayes simultaneous estimation for several multinomial distributions. Communications in Statistics: Theory and Methods, 6, 619-630. https://doi.org/10.1080/03610927708827520
  6. 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
  7. Nandram, B. (1998). A Bayesian analysis of the three-stage hierarchical multinomial model. Journal of Statistical Computation and Simulation, 61, 97-112. https://doi.org/10.1080/00949659808811904
  8. Nandram, B. and Kim, H. (2002). Marginal likelihood for a class of Bayesian generalized linear models. Journal of Statistical Computation and Simulation, 72, 319-340. https://doi.org/10.1080/00949650212842
  9. 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
  10. 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

Cited by

  1. Bayesian test of homogenity in small areas: A discretization approach vol.28, pp.6, 2017, https://doi.org/10.7465/jkdi.2017.28.6.1547