A generic disjunctive/conjunctive decomposition model for n-ary relations

This paper discusses a generic decomposition model that represents an arbit rary n-ary relation as a disjunctive or conjunctive combination of a number of n-ary component relations of a prespecified type. An important subclass of order-preserving decompositions is defined and its properties are deriv ed. The generic model is shown to subsume various known models as special c ases, including the models of Boolean factor analysis, hierarchical classes analysis, and disjunctive/conjunctive nonmetric factor analysis Moreover, it also subsumes a broad range of new models as exemplified with a novel mo del for multidimensional parallelogram analysis and novel three-way extensi ons of nonmetric factor analysis. (C) 1999 Academic Press.