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Analysis of Contingency Tables by Ideal Point Discriminant Analysis

Published online by Cambridge University Press:  01 January 2025

Yoshio Takane
Yoshio Takane*
Affiliation:
McGill University
*
Requests for reprints should be sent to Yoshio Takane, Department of Psychology, McGill University, 1205 Dr. Penfield Avenue, Montreal, Quebec, H3A 1B1, CANADA.
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Abstract

Cross-classified data are frequently encountered in behavioral and social science research. The loglinear model and dual scaling (correspondence analysis) are two representative methods of analyzing such data. An alternative method, based on ideal point discriminant analysis (DA), is proposed for analysis of contingency tables, which in a certain sense encompasses the two existing methods. A variety of interesting structures can be imposed on rows and columns of the tables through manipulations of predictor variables and/or as direct constraints on model parameters. This, along with maximum likelihood estimation of the model parameters, allows interesting model comparisons. This is illustrated by the analysis of several data sets.

Keywords

Multidimensional scalingmodel evaluationAICthe loglinear modeldual scaling (correspondence analysis)canonical analysisthe RC association model
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 4 , December 1987 , pp. 493 - 513
Copyright
Copyright © 1987 The Psychometric Society

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Footnotes

Presented as the Presidential Address to the Psychometric Society's Annual and European Meetings, June, 1987. Preparation of this paper was supported by grant A6394 from the Natural Sciences and Engineering Research Council of Canada. Thanks are due to Chikio Hayashi of University of the Air in Japan for providing the ISM data, and to Jim Ramsay and Ivo Molenaar for their helpful comments on an earlier draft of this paper.

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