Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-08T13:38:17.371Z Has data issue: false hasContentIssue false
  • English
  • Français

The Choice of Constraints in Correspondence Analysis

Published online by Cambridge University Press:  01 January 2025

Harvey Goldstein
Harvey Goldstein*
Affiliation:
University of London Institute of Education
*
Requests for reprints should be sent to Harvey Goldstein, Institute of Education, 20 Bedford Way, London WC1H OAL, ENGLAND.
Get access Rights & Permissions [Opens in a new window]

Abstract

A discussion of alternative constraint systems has been lacking in the literature on correspondence analysis and related techniques. This paper reiterates earlier results that an explicit choice of constraints has to be made which can have important effects on the resulting scores. The paper also presents new results on dealing with missing data and probabilistic category assignment.

Keywords

constraint systemscorrespondence analysisdual scalingmissing dataoptimal scalingprobabilistic category assignment
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 2 , March 1987 , pp. 207 - 215
Copyright
Copyright © 1987 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.)

Footnotes

I am most grateful to the following for their helpful comments. Arto Demirjian, Michael Greenacre, Michael Healy, Shizuhiko Nishisato, Roderick Mcdonald, and several anonymous referees.

References

de Leeuw, J.et al. (1984). The GIFI system of nonlinear multivariate analysis. In Diday, E.et al. (Eds.), Data analysis and informatics IV (pp. 415–424). Amsterdam: North Holland.Google Scholar
Demirjian, A., Goldstein, H. (1976). New systems for dental maturity based on seven and four teeth. Annals of Human Biology, 3, 411–421.CrossRefGoogle ScholarPubMed
Greenacre, M. J. (1984). Theory and applications of correspondence analysis, New York: Academic Press.Google Scholar
Healy, M. J. R., Goldstein, H. (1976). An approach to the scaling of categorised attributes. Biometrika, 63, 219–229.CrossRefGoogle Scholar
McDonald, R. P. (1983). Alternative weights and invariant parameters in optimal scaling. Psychometrika, 48, 377–392.CrossRefGoogle Scholar
McDonald, R. P., & Goldstein, H. (In preparation). Comparative properties of alternative constraint systems in optimal scaling.Google Scholar
Nishisato, S. (1980). Analysis of categorical data: Dual scaling and its applications, Toronto: University of Toronto Press.CrossRefGoogle Scholar
Tenenhaus, M., Young, F. W. (1985). An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data. Psychometrika, 50, 91–119.CrossRefGoogle Scholar