Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Correlation plot for a contingency table

  • Hong, Chong Sun (Department of Statistics, Sungkyunkwan University) ;
  • Oh, Tae Gyu (Department of Statistics, Sungkyunkwan University)
  • Received : 2021.01.29
  • Accepted : 2021.03.18
  • Published : 2021.05.31
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Abstract

Most graphical representation methods for two-dimensional contingency tables are based on the frequencies, probabilities, association measures, and goodness-of-fit statistics. In this work, a method is proposed to represent the correlation coefficients for each of the two selected levels of the row and column variables. Using the correlation coefficients, one can obtain the vector-matrix that represents the angle corresponding to each cell. Thus, these vectors are represented as a unit circle with angles. This is called a CC plot, which is a correlation plot for a contingency table. When the CC plot is used with other graphical methods as well as statistical models, more advanced analyses including the relationship among the cells of the row or column variables could be derived.

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References

  1. Barrowman NJ and Myers RA (2000). Still more spawner-recruitment curves: the hockey stick and its generalizations, Canadian Journal of Fisheries and Aquatic Sciences, 57, 665-676. https://doi.org/10.1139/f99-282
  2. Barrowman NJ and Myers RA (2003). Raindrop plots: a new way to display collections of likelihoods and distributions, The American Statistician, 57, 268-274. https://doi.org/10.1198/0003130032369
  3. Becker RA, Cleveland WS, and Shyu MJ (1996). The visual design and control of trellis display, Journal of computational and Graphical Statistics, 5, 123-155. https://doi.org/10.2307/1390777
  4. Cleveland WS and McGill R (1984). Graphical perception: theory, experimentation, and application to the development of graphical methods, Journal of the American statistical association, 79, 531-554. https://doi.org/10.1080/01621459.1984.10478080
  5. Cohen A (1980). On the graphical display of the significant components in two-way contingency tables, Communications in Statistics-Theory and Methods, 9, 1025-1041. https://doi.org/10.1080/03610928008827940
  6. Corsten LCA and Gabriel KR (1976). Graphical exploration in comparing variance matrices, Biometrics, 9,851-863. https://doi.org/10.2307/2529269
  7. Darroch JN, Lauritzen SL, and Speed TP (1980). Markov fields and log-linear interaction models for contingency tables, The Annals of Statistics, 8,522-539. https://doi.org/10.1214/aos/1176345006
  8. Doi M, Nakamura T, and Yamamoto E (2001). Conservative tendency of the crude odds ratio, Journal of the Japan Statistical Society, 31, 53-65. https://doi.org/10.14490/jjss1995.31.53
  9. Fienberg SE (1968). The estimation of cell probabilities in two-way contingency tables (Doctoral dissertation), Harvard University, USA
  10. Fienberg SE and Gilbert JP (1970). The geometry of a two by two contingency table, Journal of the American Statistical Association, 65, 694-701. https://doi.org/10.1080/01621459.1970.10481117
  11. Fienberg SE (1975). Perspective Canada as a social report, Social Indicators Research, 2, 153-174. https://doi.org/10.1007/BF00300533
  12. Friendly M (1991). SAS System for Statistical Graphics (1st ed), SAS Publishing, USA.
  13. Friendly M (1992). Mosaic displays for loglinear models. In Proceedings of the Statistical Graphics Section, American Statistical Association, 61-68.
  14. Friendly M (1994). Mosaic displays for multi-way contingency tables, Journal of the American Statistical Association, 89, 190-200. https://doi.org/10.1080/01621459.1994.10476460
  15. Gabriel KR (1971). The biplot graphical display of matrices with applications to principal component analysis, Biometrika, 58, 453-467. https://doi.org/10.1093/biomet/58.3.453
  16. Gay DM (1983). Algorithm 611: subroutines for unconstrained minimization using a model / trustregion approach, ACM Transactions on Mathematical Software, 9, 503-524. https://doi.org/10.1145/356056.356066
  17. Gay DM (1984). A trust region approach to linearly constrained optimization. In Proceedings of the Numerical Analysis(Dundee 1983, pp. 171-189, ed. F.A. Lootsma), Springer, Berlin.
  18. Gower J and Hand D (1996). Biplots, Chapman and Hall, London.
  19. Hartigan JA and Kleiner B (1981). Mosaic for contingency tables, Computer Science and Statistics. In Proceedings of the 13th Symposium on the Interface (Eddy DWF ed, pp. 268-273), Springer-Verlag, New York.
  20. Hartigan JA and Kleiner B (1984). A mosaic of the television ratings, American Statisticians, 38, 32-35.
  21. Hong CS (1995). Loglinear Model, Freedom Academy, Seoul.
  22. Hong CS, Choi HJ, and Oh MG (1999). Geometric descriptions for hierarchical log-linear models, InterStat on the Internet.
  23. Hong, CS and Lee UK (2006). Graphical methods for hierarchical log-linear models, Communications for Statistical Applications and Methods, 13, 755-764. https://doi.org/10.5351/CKSS.2006.13.3.755
  24. Li X, Buechner JM, Tarwater PM, and Munoz A (2003). A diamond-shaped equiponderant graphical display of the effects of two categorical predictors on continuous outcomes, American Statisticians, 57, 193-199. https://doi.org/10.1198/0003130031883
  25. Norusis MJ (1988). SPSS-X Advanced Statistics Guide (2nd ed), SPSS, Chicago.
  26. Park M, Lee JW, Lee JB, and Song SH (2008). Several biplot methods applied to gene expression data, Journal of Statistical Planning and Inference, 138, 500--515. https://doi.org/10.1016/j.jspi.2007.06.019
  27. Pittelkow Y and Wilson S (2005). Use of principal component analysis and of the GE-biplot for the graphical exploration of gene expression data, Biometrics, 61, 630--632. https://doi.org/10.1111/j.1541-0420.2005.00366.x
  28. Trosset MW (2005). Visualizing correlation, Journal of Computational and Graphical Statistics, 14, 1-19. https://doi.org/10.1198/106186005X27004
  29. Tufte ER (1985). The visual display of quantitative information, The Journal for Healthcare Quality (JHQ), 7, 15. https://doi.org/10.1097/01445442-198507000-00012
  30. Tukey JW (1977). Exploratory Data Analysis, Addison-Wesley Publishing Company, California.
  31. Yamamoto E and Doi M (2001). Noncollapsibility of common odds ratios without/with confounding. In Bulletin of The 53rd Session of the International Statistical Institute, Seoul, Korea, 39-40.