THE CONJUNCTIVE MODEL OF HIERARCHICAL CLASSES

This paper describes the conjunctive counterpart of De Boeck and Rosen berg's hierarchical classes model. Both the original model and its con junctive counterpart represent the set-theoretical structure of a two- way two-mode binary matrix. However, unlike the original model, the ne w model represents the row-column association as a conjunctive functio n 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 sign ificance of the conjunctive model is illustrated with empirical applic ations. Finally, it is shown how conjunctive and disjunctive hierarchi cal classes models relate to Galois lattices, and how hierarchical cla sses analysis can be useful to construct lattice models of empirical d ata.