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Models for Ordinal Hierarchical Classes Analysis

Published online by Cambridge University Press:  01 January 2025

Iwin Leenen ,
Iven Van Mechelen  and
Paul De Boeck
Iwin Leenen
Affiliation:
Katholieke Universiteit Leuven
Iven Van Mechelen*
Affiliation:
Katholieke Universiteit Leuven
Paul De Boeck
Affiliation:
Katholieke Universiteit Leuven
*
Requests for reprints should be sent to Iven Van Mechelen, Department of Psychology, University of Leuven, Tiensestraat 102, B-3000 Leuven, BELGIUM. E-Mail: [email protected]
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Abstract

This paper proposes an ordinal generalization of the hierarchical classes model originally proposed by De Boeck and Rosenberg (1998). Any hierarchical classes model implies a decomposition of a two-way two-mode binary array M into two component matrices, called bundle matrices, which represent the association relation and the set-theoretical relations among the elements of both modes in M. Whereas the original model restricts the bundle matrices to be binary, the ordinal hierarchical classes model assumes that the bundles are ordinal variables with a prespecified number of values. This generalization results in a classification model with classes ordered along ordinal dimensions. The ordinal hierarchical classes model is shown to subsume Coombs and Kao's (1955) model for nonmetric factor analysis. An algorithm is described to fit the model to a given data set and is subsequently evaluated in an extensive simulation study. An application of the model to student housing data is discussed.

Keywords

hierarchical classesbinary datascalogramsimulation
Type
Articles
Information
Psychometrika , Volume 66 , Issue 3 , September 2001 , pp. 389 - 403
Copyright
Copyright © 2001 The Psychometric Society

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