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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Benzécri, J. P. et al. (1980).Practique de l'analyse des donnees [Practice of data analysis] (Vols. 1–3). Paris: Dunod.
Escoufier, Y. (1988). Beyond correspondence analysis. In H. H. Bock (Ed.),Classification and related methods of data analysis (pp. 505–514). Amsterdam: North-Holland.
Escoufier, Y., & Junca, S. (1986). Least-squares approximation of frequencies and their logarithms.International Statistical Review, 54, 279–283.
Gifi, A. (1981).Non-linear multivariate analysis. Leiden: University of Leiden.
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.
Gilula, Z., & Haberman, S. J. (1986), Canonical analysis of contingency tables by maximum likelihood.Journal of the American Statistical Association, 81, 780–788.
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.
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.
Greenacre, M. J. (1984).Theory and applications of correspondence analysis. New York: Academic Press.
Haberman, S. J. (1979).Analsysis of qualitative data (Vol. 2). New York: Academic Press.
Lebart, L., Morineau, A., & Warwick, K. M. (1984).Multivariate descriptive statistical analysis: Correspondence analysis and related techniques for large matrices. New York: Wiley.
Nishisato, S. (1980).Analysis of categorical data: Dual scaling and its applications. Toronto: University of Toronto Press.
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.
Rao, C. R. (1964). The use and interpretation of principal components analysis in applied research.Sankhya, Series A, 26, 329–358.
Takane, Y. (1987). Analysis of contingency tables by ideal point discriminant analysis.Psychometrika, 52, 493–513.
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.
van der Heijden, P. G. M., & de Leeuw, J. (1985). Correspondence analysis used complementary to loglinear analysis.Psychometrika, 50, 429–447.
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.
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.
Author information
Authors and Affiliations
Additional information
The authors are indebted to Yoshio Takane for helpful comments on a previous draft of this manuscript.
Rights and permissions
About this article
Cite this article
Böckenholt, U., Böcknholt, I. Canonical analysis of contingency tables with linear constraints. Psychometrika 55, 633–639 (1990). https://doi.org/10.1007/BF02294612
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02294612