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Indclas: A three-way hierarchical classes model

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Abstract

A three-way three-mode extension of De Boeck and Rosenberg's (1988) two-way two-mode hierarchical classes model is presented for the analysis of individual differences in binary object × attribute arrays. In line with the two-way hierarchical classes model, the three-way extension represents both the association relation among the three modes and the set-theoretical relations among the elements of each model. An algorithm for fitting the model is presented and evaluated in a simulation study. The model is illustrated with data on psychiatric diagnosis. Finally, the relation between the model and extant models for three-way data is discussed.

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References

  • Andreasen, N.C., & Olsen, S. (1982). Negativev positive schizophrenia: Definition and validation.Archives of General Psychiatry, 39, 789–794.

    Google Scholar 

  • Barbut, M., & Monjardet, B. (1970).Ordre et classification: Algèbre et combinatoire [Order and classification: Algebra combinatorics]. Paris: Hachette.

    Google Scholar 

  • Carroll, J.D., & Arabie, P. (1983). INDCLUS: An individual differences generalization of the ADCLUS model and MAPCLUS algorithm.Psychometrika, 48, 157–169.

    Google Scholar 

  • 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 

  • Carroll, J.D., & Chaturvedi, A. (1995). A general approach to clustering and multidimensional scaling of two-way, three-way, or higher-way data. In R.D. Luce, M. D'Zmura, D. Hoffman, G.J. Iverson & A.K. Romney (Eds.),Geometric representations of perceptual phenomena (pp. 295–318). Mahwah: Erlbaum.

    Google Scholar 

  • Chaturvedi, A., & Carroll, J.D. (1994). An alternating combinatorial optimization approach to fitting the INDCLUS and generalized INDCLUS models.Journal of Classification, 11, 155–170.

    Google Scholar 

  • Coombs, C.H. (1994).A theory of data. New York: Wiley.

    Google Scholar 

  • Coombs, C.H., & Kao, R.C. (1955).Nonmetric factor analysis (Engineering Research Bulletin No. 38). Ann Arbor: University of Michigan Press.

    Google Scholar 

  • De Boeck, P. (1986).HICLAS computer program: Version 1.0. Leuven: Katholieke Universiteit.

    Google Scholar 

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

    Google Scholar 

  • Harshman, R.A. (1970). Foundations of the PARAFAC procedure: Models and conditions for an “explanatory” multimodal factor analysis.UCLA Working Papers in Phonetics, 16, 1–84.

    Google Scholar 

  • Hubert, L., & Arabie, P. (1985). Comparing partitions.Journal of Classification, 2, 193–218.

    Google Scholar 

  • Jaccard, P. (1908). Nouvelles recherches sur la distribution florale [New research on floral distribution].Bulletin de la Société Vaudoise de Sciences Naturelles, 44, 223–270.

    Google Scholar 

  • Kim, K.H. (1982).Boolean matrix theory and applications. New York: Marcel Dekker.

    Google Scholar 

  • Kruskal, J.B. (1977). Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics.Linear Algebra and Its Applications, 18, 95–138.

    Google Scholar 

  • Kruskal, J.B. (1989). Rank, decomposition, and uniqueness for 3-way andN-way arrays. In R. Coppi & S. Bolasco (Eds.),Multiway data analysis (pp. 7–18). Amsterdam: North Holland.

    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: Springer-Verlag.

    Google Scholar 

  • Leenen, I., Van Mechelen, I., & De Boeck, P. (in press). A generic disjunctive/conjunctive decomposition model forn-ary relations.Journal of Mathematical Psychology.

  • Shepard, R.N., & Arabie, P. (1979). Additive clustering: Representation of similarities as combinations of discrete overlapping properties.Psychological Review, 86, 87–123.

    Google Scholar 

  • Sneath, P.H.A., & Sokal, R.R. (1973).Numerical taxonomy. San Francisco: Freeman.

    Google Scholar 

  • Stuart, G.W., Malone, V., Currie, J., Klimidis, S., & Minas, I.H. (1995). Positive and negative symptoms in neuroleptic-free psychotic inpatients.Schizophrenia Research, 16, 175–188.

    Google Scholar 

  • Van Mechelen, I. (1988). Prediction of a dichotomous criterion variable by means of a logical combination of dichotomous predictors.Mathématiques, Informatiques et Sciences Humaines, 102, 47–54.

    Google Scholar 

  • Van Mechelen, I., & De Boeck, P. (1990). Projection of a binary criterion into a model of hierarchical classes.Psychometrika, 55, 677–694.

    Google Scholar 

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

    Google Scholar 

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Correspondence to Iwin Leenen.

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The research reported in this paper was partially supported by NATO (Grant CRG.921321 to Iven Van Mechelen and Seymour Rosenberg).

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Leenen, I., Van Mechelen, I., De Boeck, P. et al. Indclas: A three-way hierarchical classes model. Psychometrika 64, 9–24 (1999). https://doi.org/10.1007/BF02294316

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  • DOI: https://doi.org/10.1007/BF02294316

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