Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Bayesian Hypothesis Testing in Multivariate Growth Curve Model.

  • Kim, Hea-Jung (Department of Statistics, Dongguk University, Seoul, 100-715) ;
  • Lee, Seung-Joo (Department of Applied Statistics, Chong-Ju University, Chong-Ju, 360-764)
  • Published : 1996.03.01
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Abstract

This paper suggests a new criterion for testing the general linear hypothesis about coefficients in multivariate growth curve model. It is developed from a Bayesian point of view using the highest posterior density region methodology. Likelihood ratio test criterion(LRTC) by Khatri(1966) results as an approximate special case. It is shown that under the simple case of vague prior distribution for the multivariate normal parameters a LRTC-like criterion results; but the degrees of freedom are lower, so the suggested test criterion yields more conservative test than is warranted by the classical LRTC, a result analogous to that of Berger and Sellke(1987). Moreover, more general(non-vague) prior distributions will generate a richer class of tests than were previously available.

Keywords

References

  1. An Introduction to Multivariate Statistical Analysis(2nd ed.) Anderson, T. W.
  2. Journal of the American Statistical Association v.82 no.397 Testing a point null hypothesis:The irreconcilability of p-values and evidence Berger, J. O.;Sellke, T.
  3. Biometrika v.36 A general distribution theory for a class of likelihood ratio criteria Box, G. E. P.
  4. Bayesian Inference in Statistical Analysis Box, G. E. P.;Tiao, G. C.
  5. Annals of Mathematical Statistics v.38 Multivariate generalizations of the multivariate t-distribution and the inverted matrix t-distribution Dickey, J. M.
  6. Sankhya, Series A. Bayesian analysis of growth curves Geisser, S.
  7. Handbook of Statistics v.2 Growth curve analysis Geisser, S.
  8. Journal of the Royal Statistical Society, Series B. v.25 Posterior distributions for multivariate normal parameters Geisser, S.;Cornfield, J.
  9. Theory of Probability(3rd ed.) Jeffreys, H.
  10. Communication in Statistics - Theory and Methods v.15 On a GMANOVA model likelihood ratio test criterion Kabe, D. G.
  11. Annals of the Institute of Statistical Mathematics v.18 A note on a MANOVA model applied to problems in growth model Khatri, C. G.
  12. Journal of the American Statistical Association v.83 Prediction and estimation of growth curves with special covariance structures Lee, J. C.
  13. Biometrika v.56 On the exact distribution of Wilks's criterion Pillai, K. C. S.;Gupta, A. K.
  14. Biometrika v.51 A generalized multivariate analysis of variance model useful especially for growth curve problems Potthoff, R. F.;Roy, S. N.
  15. Multivariate Analysis v.4 Prediction of future observations with special reference to linear models Rao, C. R.;Krishnaiah, P. R.(ed.)
  16. Proceedings of the Indian Statistical Institute Golden Jubilee International Conference on Statistics : Application and New Directions Prediction of future observations in polynomial growth curve models Rao, C. R.
  17. Statistical Science v.2 Prediction of future observations in growth curve models Rao, C. R.
  18. Biometrika v.53 Exact distributions of Wilks's likelihood ratio criterion Schatzoff, M.
  19. Journals of the American Statistical Association v.75 On application of growth curve techniques to time series data Zerbe, G. O.;Jones, R. H.