Hostname: page-component-6bf8c574d5-mggfc Total loading time: 0 Render date: 2025-02-21T07:04:34.806Z Has data issue: false hasContentIssue false
  • English
  • Français

Correspondence Analysis used Complementary to Loglinear Analysis

Published online by Cambridge University Press:  01 January 2025

Peter G. M. van der Heijden  and
Jan de Leeuw
Peter G. M. van der Heijden*
Affiliation:
Department of Methodology, University of Leiden
Jan de Leeuw
Affiliation:
Department of data theory, University of Leiden
*
Requests for reprints should be sent to P. G. M. van der Heijden, Department of Methodology, University of Leiden, Hooigracht 15, 2312 KM Leiden, THE NETHERLANDS.
Get access Rights & Permissions [Opens in a new window]

Abstract

Loglinear analysis and correspondence analysis provide us with two different methods for the decomposition of contingency tables. In this paper we will show that there are cases in which these two techniques can be used complementary to each other. More specifically, we will show that often correspondence analysis can be viewed as providing a decomposition of the difference between two matrices, each following a specific loglinear model. Therefore, in these cases the correspondence analysis solution can be interpreted in terms of the difference between these loglinear models. A generalization of correspondence analysis, recently proposed by Escofier, will also be discussed. With this decomposition, which includes classical correspondence analysis as a special case, it is possible to use correspondence analysis complementary to loglinear analysis in more instances than those described for classical correspondence analysis. In this context correspondence analysis is used for the decomposition of the residuals of specific restricted loglinear models.

Keywords

correspondence analysisdata analysisloglinear analysismulti-dimensional scaling
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 4 , December 1985 , pp. 429 - 447
Copyright
Copyright © 1985 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agresti, A. (1983). A survey of strategies for modeling cross-classifications having ordinal variables. Journal of the American Statistical Association, 78, 184–198.CrossRefGoogle Scholar
Andersen, E. B. (1980). Discrete statistical models with social science applications, Amsterdam: North Holland.Google Scholar
Benzécri, J. P. (1973). Analyse des données [The analysis of Data], Paris: Dunod.Google Scholar
Benzécri, J. P. (1980). Pratique de l'analyse des données [The Practice of Data Analysis], Paris: Dunod.Google Scholar
Bishop, Y. M., Y., Fienberg, S. E., Holland, P. W. (1975). Discrete multivariate analysis: Theory and practice, Cambridge: MIT press.Google Scholar
Bonett, D. G., Bentler, P. M. (1983). Goodness-of-fit procedures for the evaluation and selection of loglinear models. Psychological Bulletin, 93(1), 149–166.CrossRefGoogle Scholar
Daudin, J. J., Trécourt, P. (1980). Analyse factorielle des correspondances et modèle log-lineaire: Comparaison des deux methodes sur un exemple [Correspondence analysis and the loglinear model: Comparison of two methods on an example]. Revue de Statistique Appliquée, 28(1), 5–24.Google Scholar
de Leeuw, J. (1971). Canonical analysis of contingency tables (RB-002-71), Leiden: R.U.L./F.S.W., Department of Datatheory.Google Scholar
de Leeuw, J. (1983). Models and methods for the analysis of correlation coefficients. Journal of Econometrics, 22, 113–128.CrossRefGoogle Scholar
de Leeuw, J. (1984). Canonical analysis of categorical data, Leiden: DSWO-press.Google Scholar
Diekstra, R. F. W. (1981). Over suicide [about suicide], Alphen a/d Rijn: Samson.Google Scholar
Dixon, W. J. (1981). BMDP statistical software 1981, Berkeley: University of California Press.Google Scholar
Douglas, J. D. (1973). The social meanings of suicide, Princeton: Princeton University Press.Google Scholar
Escofier, B. (1983). Analyse de la difference entre deux mesures sur le produit de deux mêmes ensembles [Analysis of the difference between two measures on the product of two identical sets]. Cahiers de l'Analyse des Données, 3, 325–329.Google Scholar
Fienberg, S. E. (1980). The analysis of cross-classified categorical data 2nd ed.,, Cambridge: MIT Press.Google Scholar
Fienberg, S. E., Meyer, M. M. (1983). Loglinear models and categorical data analysis with psychometric and econometric applications. Journal of Econometrics, 22, 191–214.CrossRefGoogle Scholar
Gifi, A. (1981). Non-linear multivariate analysis (2nd. ed. in press, LeidenLeiden: R.U.L./F.S.W., Department of Datatheory DSWO press)Google Scholar
Goodman, L. A. (1979). Simple models for the analysis of association in cross-classifications having ordered categories. Journal of the American Statistical Association, 74, 537–552.CrossRefGoogle Scholar
Goodman, L. A. (1981). Association models and the bivariate normal for contingency tables with ordered categories. Biometrika, 68, 347–355.CrossRefGoogle Scholar
Goodman, L. A. (1981). Association models and canonical correlation in the analysis of cross-classifications having ordered categories. Journal of the American Statistical Association, 76, 320–334.Google Scholar
Greenacre, M. J. (1984). Theory and applications of correspondence analysis, London: Academic Press.Google Scholar
Heiser, W. J., Meulman, J. (1983). Analyzing rectangular tables by joint and constrained multi-dimensional scaling. Journal of Econometrics, 22, 139–167.CrossRefGoogle Scholar
Heuer, J. (1979). Selbstmord bei Kinder und Jugendlichen [Suicide of children and youth], Stuttgard: Ernst Klett Verlag.Google Scholar
Israëls, A. Z., Sikkel, D. (1982). Correspondence analysis and comparisons with other techniques, Voorburg: Centraal Bureau voor Statistiek.Google Scholar
Jacobs, L. (1971). Adolescent suicide, New York: Wiley.Google Scholar
Kendall, M. G., Stuart, A. (1973). The advanced theory of statistics, Vol. 2 3rd. ed.,, London: Griffin.Google Scholar
Kroonenberg, P. M. (1983). Three-mode principal component analysis, Leiden: DSWO-press.Google Scholar
Leclerc, A. (1975). L'analyse des correspondances sur juxtaposition de tableaux de contingence [Correspondence analysis of concatenated contingency tables]. Revue de Statistique Appliquée, 23(3), 5–16.Google Scholar
Nishisato, S. (1980). Analysis of categorical data: Dual scaling and its applications, Toronto: University of Toronto Press.CrossRefGoogle Scholar
Reynolds, H. T. (1977). The analysis of cross-classifications, Glencoe, IL: The Free Press.Google Scholar