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Graphical representations and Odds Ratios in a Distance-Association Model for the Analysis of Cross-Classified Data

Published online by Cambridge University Press:  01 January 2025

Mark de Rooij  and
Willem J. Heiser
Mark de Rooij*
Affiliation:
Leiden University
Willem J. Heiser
Affiliation:
Leiden University
*
Requests for reprints should be addressed to Mark de Rooij, Department of Psychology, Leiden University, PO Box 9555, 2300 RB Leiden, The Netherlands. E-mail: rooijm@fsw.leidenuniv.nl
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Abstract

Although RC(M)-association models have become a generally useful tool for the analysis of cross-classified data, the graphical representation resulting from such an analysis can at times be misleading. The relationships present between row category points and column category points cannot be interpreted by inter point distances but only through projection. In order to avoid incorrect interpretation by a distance rule, joint plots should be made that either represent the row categories or the column categories as vectors. In contrast, the present study proposes models in which the distances between row and column points can be interpreted directly, with a large (small) distance corresponding to a small (large) value for the association. The models provide expressions for the odds ratios in terms of distances, which is a feature that makes the proposed models attractive reparametrizations to the usual RC(M)-parametrization. Comparisons to existing data analysis techniques plus an overview of related models and their connections are also provided.

Keywords

Euclidean distancesmaximum likelihood estimationlog-linear modellingmultidimensional scalingmultidimensional unfolding
Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 1 , March 2005 , pp. 99 - 122
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

The authors are indebted to the reviewers, Ab Mooijaart, Patrick Groenen, and Lawrence Hubert for their comments on earlier versions of this manuscript. Netherlands Organization for Scientific Research (NWO) is gratefully acknowledged for funding this project. This research was conducted while the first author was supported by a grant of the Foundation for Behavioral and Educational Sciences of this organization (575-30-006). This paper was completed while the second author was research fellow at the Netherlands Institute in the Advanced Study in the Humanities and Social Sciences (NIAS) in Wassenaar, The Netherlands.

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