Desicom: Decomposition of Asymmetric Relationships Data into Simple Components

Abstract

DEDICOM is a method for decomposing an asymmetric data matrix with relationships among a set of objects into a loading matrix and a matrix of relationships between “underlying” aspects. In Kiers and Takane’s constrained DEDICOM the loading matrix can be constrained to have, for instance, zeros at prespecified positions. In particular, one can constrain the loading matrix such that it has only one nonzero element per stimulus, thus assigning the objects into (prespecified) simple components. Simple components here refer to components to which mutually exclusive subsets of objects are assigned. Thus, this procedure entails a partitioning of the objects into mutually exclusive clusters. In practice, it is often hard to choose the partitioning a priori. The present paper offers a procedure for finding a partitioning on the basis of the data. Specifically, in the present paper a method is proposed which partitions the objects into nonoverlapping clusters yielding the best possible fit of DESICOM (DEDICOM employing Simple components). The paper offers algorithms for finding the best simple components both on the basis of full data tables, and on the basis of data where the diagonal is to be ignored. Some technical results on the performance of the algorithms are given, and the method is illustrated by means of the analysis of two empirical data sets.