Seriation and multidimensional scaling: A data analysis approach to scaling asymmetric proximity matrices

Abstract

A number of model-based scaling methods have been developed that apply to asymmetric proximity matrices. A flexible data analysis approach is proposed that combines two psychometric procedures-seriation and multidimensional scaling (MDS). The method uses seriation to define an empirical ordering of the stimuli, and then uses MDS to scale the two separate triangles of the proximity matrix defined by this ordering. The MDS solution contains directed distances, which define an "extra" dimension that would not otherwise be portrayed, because the dimension comes from relations between the two triangles rather than within triangles. The method is particularly appropriate for the analysis of proximities containing temporal information. A major difficulty is the computational intensity of existing seriation algorithms, which is handled by defining a nonmetric seriation algorithm that requires only one complete iteration. The procedure is illustrated using a matrix of co-citations between recent presidents of the Psychometric Society. Index terms: asymmetric data, cluster analysis, combinatorial data analysis, multidimensional scaling, order analysis, proximity data, seriation, unidimensional scaling.