Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Bayesian Hypothesis Testing for Intraclass Correlation Coefficient

  • Lee, Seung-A (Department of Statistics, Kyungpook National University) ;
  • Kim, Dal-Ho (Department of Statistics, Kyungpook National University)
  • Published : 2006.12.31
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Abstract

In this paper, we consider a Bayesian model selection for the intraclass correlation coefficient in familiar data. In particular, we compare two nested models such as the independence and intraclass models using the reference prior. A criterion for testing is the Bayesian Reference Criterion by Bernardo (1999) and the Intrinsic Bayes Factor by Berger and Pericchi (1996). We provide numerical examples using simulation data sets for illustration.

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References

  1. Berger, J.O. and Bernardo, J.M. (1989). Estimating a Product of Means: Bayesian Analysis with Reference Priors. Joumal of the American Statistical Association, Vol. 84, 200-207 https://doi.org/10.2307/2289864
  2. Berger, J.O. and Bernardo, J.M. (1992). On the Development of Reference Priors. Bayesian Statistics 4 (J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith, eds.), Oxford; University Press, 35-60 (with discussion)
  3. Berger, J.O. and Pericchi, L.R. (1996). The Intrinsic Bayes Factor for Model Selection and Prediction. Joumal of the American Statistical Association, Vol. 91, 109-122 https://doi.org/10.2307/2291387
  4. Bernardo, J.M. (1979). Reference Posterior Distributions for Bayesian Inference. Joumal of the Royal Statistical Society B, Vol. 41, 113-147 (with discussion). Reprinted in Bayesian Inference (N.G. Polson and G.C. Tiao, eds.), Brookfield, VT: Edward Elgar, (1995), 229-263
  5. Bernardo, J.M. (1999). Nested Hypothesis Testing : The Bayesian Reference Criterion. Bayesian Statistics 6 (J.M. Bernardo, J.O. Berger, AP. Dawid and A.F.M. Smith, eds.). Oxford: University Press, 101-130 (with discussion)
  6. Donner, A. and Bull, S. (1983). Inference Concerning a Common Intraclass Correlation Coefficient. Biometrics, Vol. 39, 771-775 https://doi.org/10.2307/2531107
  7. Gokhale, D.V. and SenGupta, A. (1986). Optimal Tests for the Correlation Coefficient in a Symmetric Multivariate Normal Population. Journal of Statistical Planning and Inference, Vol. 14, 263-268 https://doi.org/10.1016/0378-3758(86)90164-3
  8. Huang, W. and Sinha, B.K. (1993). On Optimum Invariant Tests of Equality of Intraclass Correlation Coefficients. Annals of the Institute of Statistical Mathematics, Vol. 45, 579-597 https://doi.org/10.1007/BF00773357
  9. Kim, D.H., Kang, S.K. and Lee, W.D. (2001). Noninformative Priors for Intraclass Correlation Coefficient in Familial Data. Far East Journal of Theoretical Statistics, Vol. 5, 45-60
  10. Konishi, S. (1985). Normalizing and Variance Stabilizing Transformations for Intraclass Correlations. Annals of the Institute of Statistical Mathematics, Vol. 37, 87-94 https://doi.org/10.1007/BF02481082
  11. Konishi, S. and Gupta, A.K. (1989). Testing the Equality of Several Intraclass Correlation Coefficients. Journal of Statistical Planning and Inference, Vol. 21, 93-105 https://doi.org/10.1016/0378-3758(89)90022-0
  12. Rao, C.R. (1973). Linear Statistical Inference and Its Applications, Wiley, New York
  13. Rosner, B., Donner, A. and Hennekens, G.H. (1977). Estimation of Interclass Correlation from Familial Data. Applied Statistics, Vol. 26, 179-187 https://doi.org/10.2307/2347026
  14. Rosner, B., Donner, A. and Hennekens, G.H. (1979). Significance testing of Interclass Correlations from Familial Data. Biometrics, Vol. 35, 461-471 https://doi.org/10.2307/2530348
  15. Scheffe, H. (1959). The Analysis of Variance. Wiley, New York
  16. Srivastava, M.S. (1984). Estimation of Interclass Correlations in Familial Data. Biometrika, Vol. 71, 177-185 https://doi.org/10.1093/biomet/71.1.177
  17. Velu, R. and Rao, M.B. (1990). Estimation of parent-offspring Correlation. Biometrika, Vol. 77, 557-562 https://doi.org/10.1093/biomet/77.3.557
  18. Young, D.J. and Bhandary, M. (1998). Test for Equality of Intraclass Correlation Coefficients under Unequal Family Sizes. Biometrics, Vol. 54, 1363-1373 https://doi.org/10.2307/2533663