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.
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Adam, G., Bon, F., Capdevielle, J., & Mouriaux, R. (1970).L'ouvrier français en 1970 [The French workman in 1970]. Paris: FNSP.
Benzécri, J.P. (1973).L'Analyse des données. Vol. 2. L'Analyse des correspondances. Paris: Dunod.
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.
Böckenholt, U., & Böckenholt, I. (1990). Canonical analysis of contingency tables with linear constraints.Psychometrika, 55, 633–639.
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.
Daudin, J.J. (1980). Partial association measures and an application to qualitative regression.Biometrika, 67, 581–590.
Efron, B. (1979). Bootstrap methods: Another look at the jackknife.Annals of Statistics, 7, 1–26.
Gifi, A. (1990).Nonlinear multivariate analysis. Chichester, U.K.: Wiley.
Greenacre, M.J. (1984).Theory and applications of correspondence analysis. London: Academic Press.
Lebart, L., Morineau, A., & Warwick, K.M. (1984).Multivariate descriptive statistical analysis. New York, NY: Wiley.
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.
Nishisato, S. (1980).Analysis of categorical data: Dual scaling and its applications. Toronto, Canada: University of Toronto Press.
Nishisato, S. (1984). Forced classification: A simple application of a quantitative technique.Psychometrika, 49, 25–36.
Nishisato, S. (1994).Elements of dual scaling: An introduction to practical data analysis. Hillsdale, NJ: Lawrence Erlbaum Associates.
Ramsay, J.O. (1978). Confidence regions for multidimensional scaling analysis.Psychometrika, 43, 145–160.
Seber, G.A.F. (1984).Multivariate observations. New York, NY: Wiley.
Takane, Y., & Hwang, H. (2000). Generalized constrained canonical correlation analysis. Manuscript submitted for publication.
Takane, Y., Kiers, H., & de Leeuw, J. (1995). Component analysis with different sets of constraints on different dimensions.Psychometrika, 60, 259–280.
Takane, Y., & Shibayama, T. (1991). Principal component analysis with external information on both subjects and variables.Psychometrika, 56, 97–120.
Takane, Y., Yanai, H., & Mayekawa, S. (1991). Relationships among several methods of linearly constrained correspondence analysis.Psychometrika, 56, 667–684.
ter Braak, C.J.F. (1986). Canonical correspondence analysis: A new eigenvalue technique for multivariate direct gradient analysis.Ecology, 67, 1167–1179.
Timm, N., & Carlson, J. (1976). Part and bipartial canonical correlation analysis.Psychometrika, 41, 159–176.
van Buuren, S., & de Leeuw, J. (1992). Equality constraints in multiple correspondence analysis.Multivariate Behavioral Research, 27, 567–583.
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.
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.
Yanai, H., & Maeda, T. (2000). Partial multiple correspondence analysis.Proceedings of the International Conference on Measurement and Multivariate Analysis, 28, 110–113.
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Heungsun Hwang is now at Claes Fornell International Group. The work reported in this paper was supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the second author.
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Hwang, H., Takane, Y. Generalized constrained multiple correspondence analysis. Psychometrika 67, 211–224 (2002). https://doi.org/10.1007/BF02294843
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DOI: https://doi.org/10.1007/BF02294843