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Tucker3 Hierarchical Classes Analysis

Published online by Cambridge University Press:  01 January 2025

Eva Ceulemans ,
Iven Van Mechelen  and
Iwin Leenen
Eva Ceulemans*
Affiliation:
Katholieke Universiteity Leuven
Iven Van Mechelen
Affiliation:
Katholieke Universiteity Leuven
Iwin Leenen
Affiliation:
Katholieke Universiteity Leuven
*
Requests for reprints should be sent to Eva Ceulemans, Department of Psychology, Tiensestraat 102, B-3000 Leuven, Belgium. Email: [email protected]
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Abstract

This paper presents a new model for binary three-way three-mode data, called Tucker3 hierarchical classes model (Tucker3-HICLAS). This new model generalizes Leenen, Van Mechelen, De Boeck, and Rosenberg's (1999) individual differences hierarchical classes model (INDCLAS). Like the INDCLAS model, the Tucker3-HICLAS model includes a hierarchical classification of the elements of each mode, and a linking structure among the three hierarchies. Unlike INDCLAS, Tucker3-HICLAS (a) does not restrict the hierarchical classifications of the three modes to have the same rank, and (b) allows for more complex linking structures among the three hierarchies. An algorithm to fit the Tucker3-HICLAS model is described and evaluated in an extensive simulation study. An application of the model to hostility data is discussed.

Keywords

three-way three-mode databinary datahierarchical classesmultiway data analysisclustering
Type
Article
Information
Psychometrika , Volume 68 , Issue 3 , September 2003 , pp. 413 - 433
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

The first author is a Research Assistant of the Fund for Scientific Research–Flanders (Belgium). The research reported in this paper was partially supported by the Research Council of K.U. Leuven (GOA/2000/02). We are grateful to Kristof Vansteelandt for providing us with an interesting data set.

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