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The Conjunctive Model of Hierarchical Classes

Published online by Cambridge University Press:  01 January 2025

Iven Van Mechelen ,
Paul De Boeck  and
Seymour Rosenberg
Iven Van Mechelen*
Affiliation:
Katholieke Universiteit Leuven
Paul De Boeck
Affiliation:
Katholieke Universiteit Leuven
Seymour Rosenberg
Affiliation:
Rutgers University
*
Please send requests for reprints to Iven Van Mechelen, Department of Psychology, Tiensestraat 102, B-3000 Leuven, BELGIUM. (Email: [email protected])
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Abstract

This paper describes the conjunctive counterpart of De Boeck and Rosenberg's hierarchical classes model. Both the original model and its conjunctive counterpart represent the set-theoretical structure of a two-way two-mode binary matrix. However, unlike the original model, the new model represents the row-column association as a conjunctive function of a set of hypothetical binary variables. The conjunctive nature of the new model further implies that it may represent some conjunctive higher order dependencies among rows and columns. The substantive significance of the conjunctive model is illustrated with empirical applications. Finally, it is shown how conjunctive and disjunctive hierarchical classes models relate to Galois lattices, and how hierarchical classes analysis can be useful to construct lattice models of empirical data.

Keywords

clusteringpartial orderhierarchical classesconjunctiondisjunctiontwo-way two-mode data
Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 4 , December 1995 , pp. 505 - 521
Copyright
Copyright © 1995 The Psychometric Society

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Footnotes

The research reported in this paper was supported by NATO (Grant CRG.921321 to Iven Van Mechelen and Seymour Rosenberg) and by the Research Fund of Katholieke Universiteit Leuven (Grants PDM92/19 and POR93/3 to Iven Van Mechelen; Grants OT89/9 and F91/56 to Paul De Boeck).

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