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Hierarchical Classes Modeling of Rating Data

Published online by Cambridge University Press:  01 January 2025

Iven Van Mechelen ,
Luigi Lombardi  and
Eva Ceulemans
Iven Van Mechelen*
Affiliation:
University of Leuven
Luigi Lombardi
Affiliation:
University of Leuven and University of Trento
Eva Ceulemans
Affiliation:
University of Leuven
*
Requests for reprints should be sent to Iven Van Mechelen, Psychology Department, Tiensestraat 102, 3000, Leuven, Belgium. E-mail: [email protected]
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Abstract

Hierarchical classes (HICLAS) models constitute a distinct family of structural models for N-way N-mode data. All members of the family include N simultaneous and linked classifications of the elements of the N modes implied by the data; those classifications are organized in terms of hierarchical, if–then-type relations. Moreover, the models are accompanied by comprehensive, insightful graphical representations. Up to now, the hierarchical classes family has been limited to dichotomous or dichotomized data. In the present paper we propose a novel extension of the family to two-way two-mode rating data (HICLAS-R). The HICLAS-R model preserves the representation of simultaneous and linked classifications as well as of generalized if–then-type relations, and keeps being accompanied by a comprehensive graphical representation. It is shown to bear interesting relationships with classical real-valued two-way component analysis and with methods of optimal scaling.

Keywords

rating datahierarchical classestwo-mode clustering
Type
Theory and Methods
Information
Psychometrika , Volume 72 , Issue 4 , December 2007 , pp. 475 - 488
Copyright
Copyright © 2007 The Psychometric Society

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Footnotes

The research reported in this paper was supported by the Research Fund of the University of Leuven (GOA/00/02 and GOA/05/04) and by the Fund for Scientific Research-Flanders (project G.0146.06). Eva Ceulemans is a Post-doctoral Researcher supported by the Fund for Scientific Research, Flanders. The authors gratefully acknowledge the help of Gert Quintiens and Kaatje Bollaerts in collecting the data used in Section 4 and of Jan Schepers in additional analyses of these data.

References

Ceulemans, E., Van Mechelen, I. (2003). An algorithm for HICLAS-R models. In Schader, M., Gaul, W., Vichi, M. (Eds.), Between data science and applied data analysis (pp. 173–181). Heidelberg: Springer.CrossRefGoogle Scholar
Ceulemans, E., Van Mechelen, I. (2004). Tucker2 hierarchical classes analysis. Psychometrika, 69, 375–399.CrossRefGoogle Scholar
Ceulemans, E., Van Mechelen, I., Leenen, I. (2003). Tucker3 hierarchical classes analysis. Psychometrika, 68, 413–433.CrossRefGoogle Scholar
Ceulemans, E., Van Mechelen, I., Kuppens, P. (2004). Adapting the formal to the substantive: Constrained Tucker3-HICLAS. Journal of Classification, 21, 19–50.CrossRefGoogle Scholar
De Boeck, P., Rosenberg, S. (1988). Hierarchical classes: Model and data analysis. Psychometrika, 53, 361–381.CrossRefGoogle Scholar
Gati, I., Tversky, A. (1982). Representations of qualitative and quantitative dimensions. Journal of Experimental Psychology, 8, 325–340.Google ScholarPubMed
Gifi, A. (1990). Nonlinear multivariate analysis, New York: Wiley.Google Scholar
Jaccard, P. (1908). Nouvelles recherches sur la distribution florale. Bulletin de la Société Vaudoise Sciences Naturelles, 44, 223–270.Google Scholar
Leenen, I., Van Mechelen, I. (2001). An evaluation of two algorithms for hierarchical classes analysis. Journal of Classification, 18, 57–80.CrossRefGoogle Scholar
Leenen, I., Van Mechelen, I., De Boeck, P., Rosenberg, S. (1999). INDCLAS: A three-way hierarchical classes model. Psychometrika, 64, 9–24.CrossRefGoogle Scholar
Levin, J. (1965). Three-mode factor analysis. Psychological Bulletin, 64, 442–452.CrossRefGoogle ScholarPubMed
Van de Geer, J.P. (1993). Multivariate analysis of categorical data (2 vols.), Newbury Park: Sage.Google Scholar
Van Mechelen, I., De Boeck, P., Rosenberg, S. (1995). The conjunctive model of hierarchical classes. Psychometrika, 60, 505–521.CrossRefGoogle Scholar