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

Title & Authors
Empirical Comparisons of Disparity Measures for Partial Association Models in Three Dimensional Contingency Tables
Jeong, D.B.; Hong, C.S.; Yoon, S.H.;

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$\small{^2}$, the likelihood ratio statistic G$\small{^2}$, 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
Disparity measure;Goodness-of-fit;Hellinger distance;Log-linear model;Power divergence statistic;
Language
English
Cited by
1.
RAINDROP PLOT을 이용한 차원축소,홍종선;김범준;박지용;

응용통계연구, 2005. vol.18. 2, pp.471-485
References
1.
Journal of the Royal Statistical Society, 1935. vol.2. pp.248-252

2.
Technometrics, 1968. vol.10. pp.107-123

3.
Discrete Multivariate Analysis, 1975.

4.
Journal of the American Statistical Association, 1976. vol.71. pp.854-863

5.
Annals of Mathematical Statistics, 1952. vol.23. pp.315-345

6.
Journal of the Royal Statistical Society, 1984. vol.B46. pp.440-464

7.
Publ. math. Inst. Hungar. Acad. Sci., 1963. vol.3. pp.85-107

8.
Journal of the Royal Statistical Soc., 1979. vol.B41. pp.54-64

9.
The Analysis of Cross-Classified Categorical Data (2nd Edition), 1980.

10.
Journal of the American Statistical Association, 1964. vol.59. pp.319-352

11.
Biometrics, 1969. vol.25. pp.489-504

12.
Journal of Statistical Computation and Simulation, 1984. vol.20. pp.205-215

13.
Annals of Mathematical Statistics, 1965. vol.36. pp.369-408

14.
Journal of Statistical Computation and Simulation, 2000. vol.65. pp.43-61

15.
Journal of the American Statistical Association, 1986. vol.81. pp.483-493

16.
Journal of the American Statistical Association, 1980. vol.75. pp.336-342

17.
Journal of the American Statistical Association, 1978. vol.73. pp.253-263

18.
Asymptotic Method in Statistical Decision Theory, 1986.

19.
The Annals of Statistics, 1994. vol.22. pp.1081-1114

20.
Residual Adjustment Functions and Weighted Likelihood: A Graphical Interpretation of Robustness of Minimum Disparity Estimators, 1993.

21.
Annals of Statistics, 1975. vol.3. pp.599-616

22.
Goodness-of-Fit Statistics for Discrete Multivariate Data, 1988.

23.
Annals of Mathematical Statistics, 1956. vol.27. pp.749-757

24.
Statistics and Probability Letters, 1994. vol.19. pp.307-312

25.
Communication in Statistics, Theory and Method, 1996. vol.25. pp.211-226

26.
Journal of Statistical Computation and Simulation, 1972. vol.1. pp.1-33