Journal of mathematical psychology vol:43 issue:1 pages:102-122
This paper discusses a generic decomposition model that represents an arbitrary 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 derived. The generic model is shown to subsume various known models as special cases, 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 model for multidimensional parallelogram analysis and novel three-way extensions of nonmetric factor analysis. (C) 1999 Academic Press.