Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Empirical Comparisons of Disparity Measures for Partial Association Models in Three Dimensional Contingency Tables

  • Jeong, D.B. (Department of Information Statistics, Kangnung National University) ;
  • Hong, C.S. (Department of Statistics, Sungkyunkwan University) ;
  • Yoon, S.H. (Department of Statistics, Sungkyunkwan University)
  • Published : 2003.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

This work is concerned with comparison of the recently developed disparity measures for the partial association model in three dimensional categorical data. Data are generated by using simulation on each term in the log-linear model equation based on the partial association model, which is a proposed method in this paper. This alternative Monte Carlo methods are explored to study the behavior of disparity measures such as the power divergence statistic I(λ), the Pearson chi-square statistic X$^2$, the likelihood ratio statistic G$^2$, the blended weight chi-square statistic BWCS(λ), the blended weight Hellinger distance statistic BWHD(λ), and the negative exponential disparity statistic NED(λ) for moderate sample sizes. We find that the power divergence statistic I(2/3) and the blended weight Hellinger distance family BWHD(1/9) are the best tests with respect to size and power.

Keywords

References

  1. Journal of the Royal Statistical Society v.2 Contingency Table Interaction Bartlett, M. S.
  2. Technometrics v.10 Hypotheses of No Interaction in Multidimensional Contingency Tables Bhapker, V. P.;Koch, G. G. https://doi.org/10.2307/1266228
  3. Discrete Multivariate Analysis Bishop, Y. M. M.;Fienberg, S. E.;Holland, P. W.
  4. Journal of the American Statistical Association v.71 A Comparison of the X？, -2logR, and the Multinomial Probability Criteria for Significance Testing when Expected Frequencies are Small Chapman, J. W. https://doi.org/10.2307/2286851
  5. Annals of Mathematical Statistics v.23 The χ² Test of Goodness of Fit Cochran, W. G. https://doi.org/10.1214/aoms/1177729380
  6. Journal of the Royal Statistical Society v.B46 Multinomial Goodness-of Fit Tests Cressie, N. A. C.;Read, T. R. C.
  7. Publ. math. Inst. Hungar. Acad. Sci. v.3 Eine informations theoretische Ungleichung ihre Anwendung auf den Beweis der Ergodizit$\"{a}$t von Markoffschen Ketten Csiszar, I.
  8. Journal of the Royal Statistical Soc. v.B41 the use of chi-squared statistics for categorical data problems Fienberg, S. E.
  9. The Analysis of Cross-Classified Categorical Data (2nd Edition) Fienberg, S. E.
  10. Journal of the American Statistical Association v.59 Simple Methods for Analyzing Three-factor Interaction in Contingency Tables Goodman, L. A. https://doi.org/10.2307/2282992
  11. Biometrics v.25 Analysis of Categorical Data by Linear Models Grizzle, J. E.;Starmer, C. F.;Koch, G. G. https://doi.org/10.2307/2528901
  12. Journal of Statistical Computation and Simulation v.20 A Comparison of Tests for the Hypothesis of No Three-factor Interaction in 2×2×2 Contingency Tables Haber, M. https://doi.org/10.1080/00949658408810777
  13. Annals of Mathematical Statistics v.36 Asymptotically Optimal Test for Multinomial Distribution Hoeffding, W. https://doi.org/10.1214/aoms/1177700150
  14. Journal of Statistical Computation and Simulation v.65 Negative Exponential Disparity Family Based Goodness-of-fit Tests for Multinomial Models Jeong, D.;Sarkar, S. https://doi.org/10.1080/00949650008811989
  15. Journal of the American Statistical Association v.81 Goodness-of Fit Tests for Log-linear Models in Sparse Contingency Tables Koehler, K. J. https://doi.org/10.2307/2289239
  16. Journal of the American Statistical Association v.75 Am Empirical Investigation of Goodness-of-fit Statistics for Sparse Multinomials Koehler, K. J.;Larntz, K. https://doi.org/10.2307/2287455
  17. Journal of the American Statistical Association v.73 Small-sample Comparisons of Exact Levels for Chi-squared Goodness-of-fit Statistics Larntz, K. https://doi.org/10.2307/2286650
  18. Asymptotic Method in Statistical Decision Theory Le Cam, L.
  19. The Annals of Statistics v.22 Efficiency versus Robustness: The Case for Minimum Hellinger Distance and Related Methods Lindsay, B. G. https://doi.org/10.1214/aos/1176325512
  20. Residual Adjustment Functions and Weighted Likelihood: A Graphical Interpretation of Robustness of Minimum Disparity Estimators Lindsay, B. G.;Basu, A.;Park, C.
  21. Annals of Statistics v.3 Unified Large-sample Theory of General Chi-squared Statistics Fit Tests of Fit Moore, D. S.;Spruill, M. C.
  22. Goodness-of-Fit Statistics for Discrete Multivariate Data Read, T. R. C.;Cressie, N. A.
  23. Annals of Mathematical Statistics v.27 On the Hypothesis of No Interaction in a Multi-way Contingency Table Roy, S. N.;Kastenbaum, M. A. https://doi.org/10.1214/aoms/1177728181
  24. Statistics and Probability Letters v.19 On Disparity Based Goodness-of-fit Tests for Multinomial Models Sarkar, S.;Basu, A. https://doi.org/10.1016/0167-7152(94)90181-3
  25. Communication in Statistics, Theory and Method v.25 Small Sample Comparisons for the Blended Weight Chi-square Goodness-of-fit Test Statistics Sarkar, S.;Basu, A.;Shin, D. W. https://doi.org/10.1080/03610929608831689
  26. Journal of Statistical Computation and Simulation v.1 A Comparison of the X² and Likelihood Ratio Tests for Composite Alternatives West, E. N.;Kempthorne, O. https://doi.org/10.1080/00949657208810001