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Analysing Dependence in Large Contingency Tables: NonSymmetric Correspondence Analysis and Regression with Optimal Scaling

  • Pieter M. Kroonenberg

Summary

In this presentation a brief survey is presented of the relative merits of two alternative approaches to the problem of modelling dependence for categorical variables when they have more than a few categories. The first approach is categorical regression with optimal scaling. The other technique is nonsymmetric(al) correspondence analysis. On a very general level, it will be shown to what an extent the techniques are similar and different.

Keywords

Correspondence Analysis American Statistical Association Original Category Optimal Scaling Column Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. D’Ambra, L. and Lauro, N. C. (1989). Non symmetrical analysis of three-way contingency tables. In R. Coppi and S. Bolasco (Eds.), Multiway data analysis (pp. 96 301–315 ). Amsterdam: Elsevier.Google Scholar
  2. D’Ambra, L. and Lauro, N. C. (1992). Non symmetrical exploratory data analysis. Statistica Applicata, 4, 511–529.Google Scholar
  3. Gabriel, K. R. (1971). The biplot graphic display with application to principal component analysis, Biometrika. 58, 453–467.MathSciNetCrossRefMATHGoogle Scholar
  4. Gifi, A. (1990). Nonlinear multivariate analysis. Chicester, UK: Wiley.MATHGoogle Scholar
  5. Goodman, L. A., and Kruskal, W. H. (1954). Measures of association for cross classifications, Journal of the American Statistical Association, 49, 732–764.MATHGoogle Scholar
  6. Gray, L. N. and Williams, J. S. (1975). Goodman and Kruskal’s taub. Multiple and partial analogs. Proceedings of the Social Statistics Section of the American Statistical Association (pp. 444–448 ). Washington, DC: ASAGoogle Scholar
  7. Gray, L. N. and Williams, J. S. (1981). Goodman and Kruskal’s taub. Multiple and partial analogs Sociological Methods and Research, 10, 50–62.Google Scholar
  8. Greenacre, M. J. (1984). Theory and applications of correspondence analysis. London: Academic Press.MATHGoogle Scholar
  9. Kroonenberg, P. M. and Lombardo, R. (1998). Nonsymmetric correspondence analysis: A tool for analysing contingency tables with a dependence structure. Multivariate Behavioral Research, 34, 367–396.CrossRefGoogle Scholar
  10. Lauro, N. C. and Balbi, S. (1995). The analysis of structured qualitative data. In A. Rizzi (Ed.), Some relations between matrices and structures of multidimensional data analysis (pp. 53–92 ). Pisa, Italy: CNR.Google Scholar
  11. Lauro, N. C. and D’Ambra, L. (1984). L’Analyse non symétrique des correspondances [Nonsymmetric correspondence analysis]. In E. Diday et al. (Eds.), Data analysis and Informatics III (pp. 433–446 ). Amsterdam: Elsevier.Google Scholar
  12. Light, R. J. and Margolin, B. H. (1971). An analysis of variance for categorical data, Journal of the American Statistical Association, 66, 534–544.MathSciNetCrossRefMATHGoogle Scholar
  13. Margolin, B. H. and Light, R. J. (1974). An analysis of variance for categorical data, II: Small sample comparisons with Chi Square and other competitors, Journal of the American Statistical Association, 69, 755–764.MathSciNetCrossRefMATHGoogle Scholar
  14. Maxwell, A. E. (1961). Analyzing qualitative data. London: MethuenGoogle Scholar
  15. Meulman, J. J., Heiser, W..J., and SPSS Inc (2000) Categories 10.0. Chicago, IL: SPSS Inc.Google Scholar
  16. Ritov, Y. and Gilula, Z. (1993). Analysis of contingency tables by correspondence models subject to order constraints. Journal of the American Statistical Association, 88, 1380–1387.MathSciNetCrossRefMATHGoogle Scholar
  17. Siciliano, R. (1992). Reduced-rank models for dependence analysis of contingency tables. Statistica Applicata, 4, 481–501.Google Scholar
  18. Tucker, L.R. (1960). Intra-individual and inter-individual multidimensionality. In H. Gulliksen, S. Messick (Eds.), Psychological Scaling: Theory and applications (pp. 155–167). New York: Wiley.Google Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Pieter M. Kroonenberg
    • 1
  1. 1.Department of EducationLeiden UniversityLeidenThe Netherlands

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