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

DOI QR코드

DOI QR Code

Jeong, D.B.;Hong, C.S.;Yoon, S.H.

  • 발행 : 2003.04.01

초록

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.

키워드

Disparity measure;Goodness-of-fit;Hellinger distance;Log-linear model;Power divergence statistic

참고문헌

  1. Journal of the Royal Statistical Society v.2 pp.248-252 Contingency Table Interaction Bartlett, M. S.
  2. Annals of Mathematical Statistics v.36 pp.369-408 Asymptotically Optimal Test for Multinomial Distribution Hoeffding, W. https://doi.org/10.1214/aoms/1177700150
  3. Journal of the American Statistical Association v.73 pp.253-263 Small-sample Comparisons of Exact Levels for Chi-squared Goodness-of-fit Statistics Larntz, K. https://doi.org/10.2307/2286650
  4. Asymptotic Method in Statistical Decision Theory Le Cam, L.
  5. Journal of the American Statistical Association v.81 pp.483-493 Goodness-of Fit Tests for Log-linear Models in Sparse Contingency Tables Koehler, K. J. https://doi.org/10.2307/2289239
  6. The Annals of Statistics v.22 pp.1081-1114 Efficiency versus Robustness: The Case for Minimum Hellinger Distance and Related Methods Lindsay, B. G. https://doi.org/10.1214/aos/1176325512
  7. Annals of Mathematical Statistics v.27 pp.749-757 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
  8. Journal of the American Statistical Association v.75 pp.336-342 Am Empirical Investigation of Goodness-of-fit Statistics for Sparse Multinomials Koehler, K. J.;Larntz, K. https://doi.org/10.2307/2287455
  9. Journal of the Royal Statistical Soc. v.B41 pp.54-64 the use of chi-squared statistics for categorical data problems Fienberg, S. E.
  10. Journal of the American Statistical Association v.71 pp.854-863 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
  11. Technometrics v.10 pp.107-123 Hypotheses of No Interaction in Multidimensional Contingency Tables Bhapker, V. P.;Koch, G. G. https://doi.org/10.2307/1266228
  12. Publ. math. Inst. Hungar. Acad. Sci. v.3 pp.85-107 Eine informations theoretische Ungleichung ihre Anwendung auf den Beweis der Ergodizit$\"{a}$t von Markoffschen Ketten Csiszar, I.
  13. Journal of Statistical Computation and Simulation v.1 pp.1-33 A Comparison of the X² and Likelihood Ratio Tests for Composite Alternatives West, E. N.;Kempthorne, O. https://doi.org/10.1080/00949657208810001
  14. Communication in Statistics, Theory and Method v.25 pp.211-226 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
  15. Biometrics v.25 pp.489-504 Analysis of Categorical Data by Linear Models Grizzle, J. E.;Starmer, C. F.;Koch, G. G. https://doi.org/10.2307/2528901
  16. Annals of Statistics v.3 pp.599-616 Unified Large-sample Theory of General Chi-squared Statistics Fit Tests of Fit Moore, D. S.;Spruill, M. C.
  17. Discrete Multivariate Analysis Bishop, Y. M. M.;Fienberg, S. E.;Holland, P. W.
  18. Journal of the American Statistical Association v.59 pp.319-352 Simple Methods for Analyzing Three-factor Interaction in Contingency Tables Goodman, L. A. https://doi.org/10.2307/2282992
  19. Journal of the Royal Statistical Society v.B46 pp.440-464 Multinomial Goodness-of Fit Tests Cressie, N. A. C.;Read, T. R. C.
  20. Journal of Statistical Computation and Simulation v.65 pp.43-61 Negative Exponential Disparity Family Based Goodness-of-fit Tests for Multinomial Models Jeong, D.;Sarkar, S. https://doi.org/10.1080/00949650008811989
  21. Statistics and Probability Letters v.19 pp.307-312 On Disparity Based Goodness-of-fit Tests for Multinomial Models Sarkar, S.;Basu, A. https://doi.org/10.1016/0167-7152(94)90181-3
  22. Goodness-of-Fit Statistics for Discrete Multivariate Data Read, T. R. C.;Cressie, N. A.
  23. Residual Adjustment Functions and Weighted Likelihood: A Graphical Interpretation of Robustness of Minimum Disparity Estimators Lindsay, B. G.;Basu, A.;Park, C.
  24. Annals of Mathematical Statistics v.23 pp.315-345 The χ² Test of Goodness of Fit Cochran, W. G. https://doi.org/10.1214/aoms/1177729380
  25. The Analysis of Cross-Classified Categorical Data (2nd Edition) Fienberg, S. E.
  26. Journal of Statistical Computation and Simulation v.20 pp.205-215 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