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Projection of a Binary Criterion into a Model of Hierarchical Classes

Published online by Cambridge University Press:  01 January 2025

Iven Van Mechelen  and
Paul De Boeck
Iven Van Mechelen*
Affiliation:
University of Leuven
Paul De Boeck
Affiliation:
University of Leuven
*
Requests for reprints should be sent to Iven Van Mechelen, Department of Psychology, University of Leuven, Tiensestraat 102, B-3000 Leuven, BELGIUM.
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Abstract

A formal analysis is made of how to project an attribute criterion into the hierarchical classes model for object by attribute data proposed by De Boeck and Rosenberg. The projection is conceptualized as the prediction of the attribute criterion by means of a logical rule defined on the basis of attribute combinations from the model. Eliminative and constructive strategies are proposed to find logical rules with maximal predictive power and minimal formula complexity. Logical analyses of a real data set are reported and compared with a logistic regression to demonstrate the usefulness of the logical strategies, and to show the complementarity of logical and probabilistic approaches.

Keywords

hierarchical classeslogical combinationsminimization of Boolean functions
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 4 , December 1990 , pp. 677 - 694
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

The first author is Senior Research Assistant of the National Fund for Scientific Research (Belgium). We would like to thank the Editor, the reviewers, Seymour Rosenberg, and Luc Delbeke for their helpful comments on earlier drafts of this article.

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