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Psychometrika

, Volume 67, Issue 2, pp 211–224 | Cite as

Generalized constrained multiple correspondence analysis

  • Heungsun Hwang
  • Yoshio Takane
Articles

Abstract

A comprehensive approach for imposing both row and column constraints on multivariate discrete data is proposed that may be called generalized constrained multiple correspondence analysis (GCMCA). In this method each set of discrete data is first decomposed into several submatrices according to its row and column constraints, and then multiple correspondence analysis (MCA) is applied to the decomposed submatrices to explore relationships among them. This method subsumes existing constrained and unconstrained MCA methods as special cases and also generalizes various kinds of linearly constrained correspondence analysis methods. An example is given to illustrate the proposed method.

Key words

multiple correspondence analysis linear constraints projection operators generalized singular value decomposition 

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References

  1. Adam, G., Bon, F., Capdevielle, J., & Mouriaux, R. (1970).L'ouvrier français en 1970 [The French workman in 1970]. Paris: FNSP.Google Scholar
  2. Benzécri, J.P. (1973).L'Analyse des données. Vol. 2. L'Analyse des correspondances. Paris: Dunod.Google Scholar
  3. Benzécri, J.P. (1979). Sur le calcul des taux d'inertia dans l'analyse d'un questionaire. Addendum et erratum à.Cahiers de L'analyse des Données, 4, 377–378.Google Scholar
  4. Böckenholt, U., & Böckenholt, I. (1990). Canonical analysis of contingency tables with linear constraints.Psychometrika, 55, 633–639.Google Scholar
  5. Böckenholt, U., & Takane, Y. (1994). Linear constraints in correspondence analysis. In M.J. Greenacre & J. Blasius (Eds.),Correspondence analysis in social sciences (pp. 112–127). London: Academic Press.Google Scholar
  6. Daudin, J.J. (1980). Partial association measures and an application to qualitative regression.Biometrika, 67, 581–590.Google Scholar
  7. Efron, B. (1979). Bootstrap methods: Another look at the jackknife.Annals of Statistics, 7, 1–26.Google Scholar
  8. Gifi, A. (1990).Nonlinear multivariate analysis. Chichester, U.K.: Wiley.Google Scholar
  9. Greenacre, M.J. (1984).Theory and applications of correspondence analysis. London: Academic Press.Google Scholar
  10. Lebart, L., Morineau, A., & Warwick, K.M. (1984).Multivariate descriptive statistical analysis. New York, NY: Wiley.Google Scholar
  11. Le Roux, B., & Rouanet, H. (1998). Interpreting axes in multiple correspondence analysis: Method of the contributions of points and deviations. In M.J. Greenacre & J. Blasius (Eds.),Visualization of categorical data (pp. 197–220). Chestnut Hill, MA: Academic Press.Google Scholar
  12. Nishisato, S. (1980).Analysis of categorical data: Dual scaling and its applications. Toronto, Canada: University of Toronto Press.Google Scholar
  13. Nishisato, S. (1984). Forced classification: A simple application of a quantitative technique.Psychometrika, 49, 25–36.Google Scholar
  14. Nishisato, S. (1994).Elements of dual scaling: An introduction to practical data analysis. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  15. Ramsay, J.O. (1978). Confidence regions for multidimensional scaling analysis.Psychometrika, 43, 145–160.Google Scholar
  16. Seber, G.A.F. (1984).Multivariate observations. New York, NY: Wiley.Google Scholar
  17. Takane, Y., & Hwang, H. (2000). Generalized constrained canonical correlation analysis. Manuscript submitted for publication.Google Scholar
  18. Takane, Y., Kiers, H., & de Leeuw, J. (1995). Component analysis with different sets of constraints on different dimensions.Psychometrika, 60, 259–280.Google Scholar
  19. Takane, Y., & Shibayama, T. (1991). Principal component analysis with external information on both subjects and variables.Psychometrika, 56, 97–120.Google Scholar
  20. Takane, Y., Yanai, H., & Mayekawa, S. (1991). Relationships among several methods of linearly constrained correspondence analysis.Psychometrika, 56, 667–684.Google Scholar
  21. ter Braak, C.J.F. (1986). Canonical correspondence analysis: A new eigenvalue technique for multivariate direct gradient analysis.Ecology, 67, 1167–1179.Google Scholar
  22. Timm, N., & Carlson, J. (1976). Part and bipartial canonical correlation analysis.Psychometrika, 41, 159–176.Google Scholar
  23. van Buuren, S., & de Leeuw, J. (1992). Equality constraints in multiple correspondence analysis.Multivariate Behavioral Research, 27, 567–583.Google Scholar
  24. Yanai, H. (1986). Some generalizations of correspondence analysis in terms of projection operators. In E. Diday, Y. Escoufier, L. Lebart, J. P. Pagès, Y. Schektman, & R. Thomassone (Eds.),Data analysis and informatics IV (pp. 193–207). Amsterdam: North Holland.Google Scholar
  25. Yanai, H. (1998). Generalized canonical correlation analysis with linear constraints. In C. Hayashi, N. Ohsumi, K. Yajima, Y. Tanaka, H.-H. Bock, & Y. Baba (Eds.),Data science, classification, and related methods (pp. 539–546). Tokyo: Springer-Verlag.Google Scholar
  26. Yanai, H., & Maeda, T. (2000). Partial multiple correspondence analysis.Proceedings of the International Conference on Measurement and Multivariate Analysis, 28, 110–113.Google Scholar

Copyright information

© The Psychometric Society 2002

Authors and Affiliations

  1. 1.McGill UniversityUSA

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