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Tucker2 Hierarchical Classes Analysis

Published online by Cambridge University Press:  01 January 2025

Eva Ceulemans  and
Iven Van Mechelen
Eva Ceulemans*
Affiliation:
Katholieke Universiteit Leuven
Iven Van Mechelen
Affiliation:
Katholieke Universiteit Leuven
*
Correspondence concerning this paper should be addressed to Eva Ceulemans, Department of Psychology, Tiensestraat 102, B-3000 Leuven, Belgium. Email: Eva.Ceulemans@psy.kuleuven.ac.be.
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Abstract

This paper presents a new hierarchical classes model, called Tucker2-HICLAS, for binary three-way three-mode data. As any three-way hierarchical classes model, the Tucker2-HICLAS model includes a representation of the association relation among the three modes and a hierarchical classification of the elements of each mode. A distinctive feature of the Tucker2-HICLAS model, being closely related to the Tucker3-HICLAS model (Ceulemans, Van Mechelen & Leenen, 2003), is that one of the three modes is minimally reduced and, hence, that the differences among the association patterns of the elements of this mode are maximally retained in the model. Moreover, as compared to Tucker3-HICLAS, Tucker2-HICLAS implies three rather than four different types of parameters and as such is simpler to interpret. Two types of Tucker2-HICLAS models are distinguished: a disjunctive and a conjunctive type. An algorithm for fitting the Tucker2-HICLAS model is described and evaluated in a simulation study. The model is illustrated with longitudinal data on interpersonal emotions.

Keywords

three-way three-mode databinary datahierarchical classesmultiway data analysisclustering
Type
Theory and Methods
Information
Psychometrika , Volume 69 , Issue 3 , September 2004 , pp. 375 - 399
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

The first author is a Researcher 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). The authors are grateful to Iwin Leenen for the fruitful discussions.

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