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Canonical analysis of contingency tables with linear constraints

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Abstract

A generalized least squares approach is presented for incorporating linear constraints on the standardized row and column scores obtained from a canonical analysis of a contingency table. The method is easy to implement and may simplify considerably the interpretation of a data matrix. The approach is compared to a restricted maximum likelihood procedure.

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References

  • Benzécri, J. P. et al. (1980).Practique de l'analyse des donnees [Practice of data analysis] (Vols. 1–3). Paris: Dunod.

    Google Scholar 

  • Escoufier, Y. (1988). Beyond correspondence analysis. In H. H. Bock (Ed.),Classification and related methods of data analysis (pp. 505–514). Amsterdam: North-Holland.

    Google Scholar 

  • Escoufier, Y., & Junca, S. (1986). Least-squares approximation of frequencies and their logarithms.International Statistical Review, 54, 279–283.

    Google Scholar 

  • Gifi, A. (1981).Non-linear multivariate analysis. Leiden: University of Leiden.

    Google Scholar 

  • Gilula, Z. (1982). A note on the analysis of association in cross-classifications having ordered categories.Communications in Statistics, Part A: Theory and Methods, 11, 1233–1240.

    Google Scholar 

  • Gilula, Z., & Haberman, S. J. (1986), Canonical analysis of contingency tables by maximum likelihood.Journal of the American Statistical Association, 81, 780–788.

    Google Scholar 

  • Gilula, Z., & Haberman, S. J. (1988). The analysis of multivariate contingency tables by restricted canonical and restricted association models.Journal of the American Statistical Association, 83, 760–771.

    Google Scholar 

  • Goodman, L. (1985). The analysis of cross-correlated data having ordered and/or unordered categories: Association models, correlatin models, and asymmetry models for contingency tables with or without missing entries.The Annals of Statistics, 13, 10–69.

    Google Scholar 

  • Greenacre, M. J. (1984).Theory and applications of correspondence analysis. New York: Academic Press.

    Google Scholar 

  • Haberman, S. J. (1979).Analsysis of qualitative data (Vol. 2). New York: Academic Press.

    Google Scholar 

  • Lebart, L., Morineau, A., & Warwick, K. M. (1984).Multivariate descriptive statistical analysis: Correspondence analysis and related techniques for large matrices. New York: Wiley.

    Google Scholar 

  • Nishisato, S. (1980).Analysis of categorical data: Dual scaling and its applications. Toronto: University of Toronto Press.

    Google Scholar 

  • Nishisato, S., & Lawrence (1989). Dual scaling of multiway data matrices: Several variants. In R. Coppi & S. Bolasco (Eds.),Multiway data analysis (pp. 317–326). Amsterdam: North Holland.

    Google Scholar 

  • Rao, C. R. (1964). The use and interpretation of principal components analysis in applied research.Sankhya, Series A, 26, 329–358.

    Google Scholar 

  • Takane, Y. (1987). Analysis of contingency tables by ideal point discriminant analysis.Psychometrika, 52, 493–513.

    Google Scholar 

  • Takane, Y., & Shibayama. (in press). Principal component analysis with external information on both subjects and variables.Psychometrika.

  • ter Braak, C. J. F. (1988). Partial canonical correspondence analysis. In H. H. Bock (Ed.),Classification and related methods of data analysis (pp. 551–558). Amsterdam: North-Holland.

    Google Scholar 

  • van der Heijden, P. G. M., & de Leeuw, J. (1985). Correspondence analysis used complementary to loglinear analysis.Psychometrika, 50, 429–447.

    Google Scholar 

  • van der Heijden, P. G. M., de Falguerolles, A., & de Leeuw, J. (1989). A combined approach of contingency tables analysis using correspondence analysis and loglinear analysis.Applied Statistics, 38, 249–292.

    Google Scholar 

  • Yanai, H. (1988). Partial correspondence analysis and its properties. In C. Hayashi, M. Jambu, E. Diday, & N. Ohsumi (Eds.),Recent developments in clustering and data analysis (pp. 259–266). Boston: Academic Press.

    Google Scholar 

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The authors are indebted to Yoshio Takane for helpful comments on a previous draft of this manuscript.

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Böckenholt, U., Böcknholt, I. Canonical analysis of contingency tables with linear constraints. Psychometrika 55, 633–639 (1990). https://doi.org/10.1007/BF02294612

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  • DOI: https://doi.org/10.1007/BF02294612

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