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Canonical Analysis of Contingency Tables with Linear Constraints

Published online by Cambridge University Press:  01 January 2025

Ulf Böckenholt  and
Ingo Böcknholt
Ulf Böckenholt*
Affiliation:
University of Illinois, Champaign-Urbana
Ingo Böcknholt
Affiliation:
University of Karlsruhe
*
Requests for reprints should be addressed to Ulf Böckenholt, Department of Psychology, University of Illinois at Urbana-Champaign, 603 East Daniel Street, Champaign, IL 61820.
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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.

Keywords

canonical analysissingular value decompositionrestricted maximum likelihood

Information

Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 4 , December 1990 , pp. 633 - 639
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

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

References

Benzécri, J. P. et al. (1980). Practique de l'analyse des donnees [Practice of data analysis], Paris: Dunod.Google Scholar
Escoufier, Y. (1988). Beyond correspondence analysis. In Bock, H. H. (Eds.), 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Gilula, Z., & Haberman, S. J. (1986). Canonical analysis of contingency tables by maximum likelihood. Journal of the American Statistical Association, 81, 780–788.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Nishisato, S., & Lawrence, (1989). Dual scaling of multiway data matrices: Several variants. In Coppi, R. & Bolasco, S. (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.CrossRefGoogle Scholar
Takane, Y., & Shibayama, . (in press). Principal component analysis with external information on both subjects and variables. Psychometrika.Google Scholar
ter Braak, C. J. F. (1988). Partial canonical correspondence analysis. In Bock, H. H. (Eds.), 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Yanai, H. (1988). Partial correspondence analysis and its properties. In Hayashi, C., Jambu, M., Diday, E., & Ohsumi, N. (Eds.), Recent developments in clustering and data analysis (pp. 259–266). Boston: Academic Press.CrossRefGoogle Scholar