Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Hierarchical Classes Modeling of Rating Data

  • 114 Accesses

  • 9 Citations

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.

This is a preview of subscription content, log in to check access.

References

  1. Ceulemans, E., & Van Mechelen, I. (2003). An algorithm for HICLAS-R models. In: M. Schader, W. Gaul, & M. Vichi (Eds.), Between data science and applied data analysis (pp. 173–181). Heidelberg: Springer.

  2. Ceulemans, E., & Van Mechelen, I. (2004). Tucker2 hierarchical classes analysis. Psychometrika, 69, 375–399.

  3. Ceulemans, E., Van Mechelen, I., & Leenen, I. (2003). Tucker3 hierarchical classes analysis. Psychometrika, 68, 413–433.

  4. Ceulemans, E., Van Mechelen, I., & Kuppens, P. (2004). Adapting the formal to the substantive: Constrained Tucker3-HICLAS. Journal of Classification, 21, 19–50.

  5. De Boeck, P., & Rosenberg, S. (1988). Hierarchical classes: Model and data analysis. Psychometrika, 53, 361–381.

  6. Gati, I., & Tversky, A. (1982). Representations of qualitative and quantitative dimensions. Journal of Experimental Psychology, 8, 325–340.

  7. Gifi, A. (1990). Nonlinear multivariate analysis. New York: Wiley.

  8. Jaccard, P. (1908). Nouvelles recherches sur la distribution florale. Bulletin de la Société Vaudoise Sciences Naturelles, 44, 223–270.

  9. Leenen, I., & Van Mechelen, I. (2001). An evaluation of two algorithms for hierarchical classes analysis. Journal of Classification, 18, 57–80.

  10. Leenen, I., Van Mechelen, I., De Boeck, P., & Rosenberg, S. (1999). INDCLAS: A three-way hierarchical classes model. Psychometrika, 64, 9–24.

  11. Levin, J. (1965). Three-mode factor analysis. Psychological Bulletin, 64, 442–452.

  12. Van de Geer, J.P. (1993). Multivariate analysis of categorical data (2 vols.). Newbury Park: Sage.

  13. Van Mechelen, I., De Boeck, P., & Rosenberg, S. (1995). The conjunctive model of hierarchical classes. Psychometrika, 60, 505–521.

Download references

Author information

Correspondence to Iven Van Mechelen.

Additional information

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.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

Keywords

  • rating data
  • hierarchical classes
  • two-mode clustering