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.
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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.
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Van Mechelen, I., Lombardi, L. & Ceulemans, E. Hierarchical Classes Modeling of Rating Data. Psychometrika 72, 475–488 (2007). https://doi.org/10.1007/s11336-007-9018-z
- rating data
- hierarchical classes
- two-mode clustering