Tucker2 hierarchical classes analysis
- 94 Downloads
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.
Key wordsthree-way three-mode data binary data hierarchical classes multiway data analysis clustering
Unable to display preview. Download preview PDF.
- Carroll, J.D., & Chang, J.J. (1970). Analysis of individual differences in multidimensional scaling via ann-way generalization of “Eckart-Young” decomposition.Psychometrika, 35, 283–319.Google Scholar
- Haggard, E.A. (1958).Intraclass correlation and the analysis of variance. New York: Dryden.Google Scholar
- Harshman, R.A. (1970). Foundations of theparafac procedure: Models and conditions for an explanatory multi-modal factor analysis. UCLAWorking Papers in Phonetics, 16, 1–84.Google Scholar
- Izard, C.E. (1977)Human emotions. New York: Plenum Press.Google Scholar
- Kim, K.H. (1982).Boolean matrix theory. New York: Marcel Dekker.Google Scholar
- Kirk, R.E. (1982).Experimental design: Procedures for the behavioral sciences (2nd ed.). Belmont, CA: Brooks/Cole.Google Scholar
- Kroonenberg, P.M. (1983).Three-mode principal component analysis: Theory and applications. Leiden: DSWO.Google Scholar
- Kroonenberg, P.M., & De Leeuw, J. (1980). Principal component analysis of three-mode data by means of alternating least squares algorithms.Psychometrika, 54, 69–97.Google Scholar
- Leenen, I., & Van Mechelen, I. (1998). A branch-and-bound algorithm for Boolean regression. In I. Balderjahn, R. Mathar, & M. Schader (Eds.),Data highways and information flooding, a challenge for classification and data analysis (pp. 164–171). Berlin, Germany: Springer-Verlag.Google Scholar
- Plutchik, R. (1962).The emotions: Facts, theories, and a new model. New York: Random House.Google Scholar