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Applications of Diamond Graph

다이아몬드 그래프의 활용 방법

  • Hong C.S. (Department of Statistics, SungKyunKwan University) ;
  • Ko Y.S. (Department of Statistics, SungKyunKwan University)
  • 홍종선 (성균관대학교 경제학부 통계학전공) ;
  • 고용석 (성균관대학교 통계학과)
  • Published : 2006.07.01

Abstract

There are lots of two and three dimensional graph representing two dimensional categorical data. Among them, Li, et al. (2003) proposed Diamond Graph that projects three dimensional graph into two dimension whereby the third dimension is replaced with a diamond shape whose area and middle and vertical and horizontal lengths represent the outcome. In this paper, we use the Diamond graph to test the independence of two predictor variables for two dimensional data. And this graph could be applied for finding the best fitted log-linear model to three dimensional data.

이차원 범주형 자료를 시각적으로 표현하는 이차원과 삼차원 그래프는 많이 존재한다. 그중에서 Li등(2003)은 삼차원 그래프를 이차원 평면에 투영시키는 다이아몬드 그래프를 제안하였다. 여기서 세번째 차원은 면적과 높이 그리고 길이가 관찰값에 대응하는 다이아몬드 모양으로 대체하였다. 본 논문에 서는 이차원 자료에 대하여는 두 범주형 변수의 독립성을 검정하기 위하여 다이아몬드 그래프를 이용한다. 그리고 삼차원 이상의 자료에 대해서는 자료에 가장 적합한 로그선형모형을 설정하는데 활용할 수 있다.

Keywords

References

  1. 홍종선, 최현집(1999). 범주형 자료분석, 자유아카데미
  2. Becker, R. A., Cleveland, W. S., and Shyu, M. J. (1996). The Visual Design and Control of Trellis Display, Journal of Computational and Statistical Graphics, 5, 123-155 https://doi.org/10.2307/1390777
  3. Bickel, P. J., Hammel, E. A., and O'Connell, J. W. (1975). Sex bias in graduate admissions: Data from Berkeley, Science, 187, 398-404
  4. Cleveland, W. S. and McGill, R. (1984). Graphical Perception : Theory, Experimentation, and Application to the Development of Graphical Methods, Journal of the American Statistical Association, 79, 387, 531-554 https://doi.org/10.2307/2288400
  5. Cohen, A. (1980). On the Graphical Display of the Significant Components in a Two-way Contingency Table, Communications in Statistics- Theory and Methods, A9, 1025- 1041
  6. Friendly, M. (1991). The SAS System for Statistical Graphics, Cary, NC: SAS Institute Inc.
  7. Friendly, M. (1994a). Mosaic Displays for Multi-way Contingency Tables, Journal of the American Statistical Association, 89, 190-200 https://doi.org/10.2307/2291215
  8. Friendly, M. (1994b). SAS/IML Graphics for Fourfold Displays, Observations, 3, 4, 47-56
  9. Harris, R. L. (1999). Information Graphics: A Comprehensive Illustrated Reference, New York: Oxford University Press
  10. Hartigan, J. A. and Kleiner, B. (1981). Mosaics for Contingency Tables, In W. F. Eddy (Ed.), Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface, New York: Springer-Verlag
  11. Hartigan, J. A. and Kleiner, B. (1984). A Mosaic of Television Ratings, The American Statistician, 38, 32-35 https://doi.org/10.2307/2683556
  12. Hong, C. S. and Lee, J. C. (2000). Ring Chart II for Multidimensional Categorical Data Analysing using Conditional Ring Charts, Korean Journal of Applied Statistics, 13, 1, 163-178
  13. Li, X., Buechner, J. M., Tarwater, P. M., and Munoz, A. (2003). A Diamond-Shaped Equiponderant Graphical Display of the Effects of Two Predicts on Continuous Outcomes, The American Statistician, 57, 193-199 https://doi.org/10.1198/0003130031883
  14. Oh, M. G., Hong, C. S., and Lee, J. C. (1999). Ring Chart for Categorical Data, Korean Journal of Applied Statistics, 12, 1, 225-240
  15. Tufte, E. R. (1983). The Visual Display of Quantitative Information, Cheshire, CT: Graphics Press
  16. Wilkinson, L. (1999). The Grammar of Graphics, New York: Springer-Verlag