DOI: 10.1007/S11336-007-9018-Z HIERARCHICAL CLASSES MODELING OF RATING DATA

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 el-ements 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 rep-resentations. 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 classifica-tions 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. Key words: rating data, hierarchical classes, two-mode clustering. The family of hierarchical classes (acronym: HICLAS) models, as introduced by De Boeck and Rosenberg (1988), and further extended by Van Mechelen et al. (1995), Leenen et al. (1999), Ceulemans et al. (2003), and Ceulemans and Van Mechelen (2004), constitutes a distinct family of structural models for binary N-way N-mode data D. Hierarchical classes analysis of a binar