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Correspondence Analysis of Incomplete Contingency Tables

Published online by Cambridge University Press:  01 January 2025

Jan de Leeuw  and
Peter G. M. van der Heijden
Jan de Leeuw
Affiliation:
Department of Data Theory, University of Leiden
Peter G. M. van der Heijden*
Affiliation:
Department of Psychometrics, University of Leiden
*
Requests for reprints should be sent to Peter G. M. van der Heijden, Department of Psychometrics, Subfaculty of Psychology, Faculty of Social Sciences, University of Leiden, Hooigracht 15, 2312 KM Leiden, THE NETHERLANDS.
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Abstract

Correspondence analysis can be described as a technique which decomposes the departure from independence in a two-way contingency table. In this paper a form of correspondence analysis is proposed which decomposes the departure from the quasi-independence model. This form seems to be a good alternative to ordinary correspondence analysis in cases where the use of the latter is either impossible or not recommended, for example, in case of missing data or structural zeros. It is shown that Nora's reconstitution of order zero, a procedure well-known in the French literature, is formally identical to our correspondence analysis of incomplete tables. Therefore, reconstitution of order zero can also be interpreted as providing a decomposition of the residuals from the quasi-independence model. Furthermore, correspondence analysis of incomplete tables can be performed using existing programs for ordinary correspondence analysis.

Keywords

Correspondence analysisdata analysisquasi-independencestructural zeros
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 2 , June 1988 , pp. 223 - 233
Copyright
Copyright © 1988 The Psychometric Society

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