Hierarchical classes: Model and data analysis |
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Authors: | Paul De Boeck Seymour Rosenberg |
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Institution: | (1) Department of Psychology, University of Leuven, Tiensestraat 102, 3000 Leuven, Belgium;(2) Department of Psychology, Kilmer Campus—Tillett Hall, Rutgers University, 08903 New Brunswick, NJ |
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Abstract: | A discrete, categorical model and a corresponding data-analysis method are presented for two-way two-mode (objects × attributes) data arrays with 0, 1 entries. The model contains the following two basic components: a set-theoretical formulation of the relations among objects and attributes; a Boolean decomposition of the matrix. The set-theoretical formulation defines a subset of the possible decompositions as consistent with it. A general method for graphically representing the set-theoretical decomposition is described. The data-analysis algorithm, dubbed HICLAS, aims at recovering the underlying structure in a data matrix by minimizing the discrepancies between the data and the recovered structure. HICLAS is evaluated with a simulation study and two empirical applications.This research was supported in part by a grant from the Belgian NSF (NFWO) to Paul De Boeck and in part by NSF Grant BNS-83-01027 to Seymour Rosenberg. We thank Iven Van Mechelen for clarifying several aspects of the Boolean algebraic formulation of the model and Phipps Arabie for his comments on an earlier draft. |
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Keywords: | binary data Boolean algebra hierarchical classes set-theoretical model two-way two-mode matrices |
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