A New Multidimensional Scaling Methodology for the Analysis of Asymmetric Proximity Data in Marketing Research

This paper presents a new multidimensional scaling (MDS) methodology which operationalizes the Krumhansl (1978) distance-density model for the analysis of asymmetric proximity data. In Krumhansl's conceptualization, the symmetric Euclidean interbrand distances typically associated with the traditional MDS model are augmented by the spatial density around the brands in the derived space. This modification allows the distance-density model to accommodate many of the empirically observed violations of the metric axioms (such as asymmetry). An operationalization of the distance-density model is particularly attractive to marketers who often work with asymmetric brand switching data to investigate market structure and competition. We describe this new MDS procedure which is sufficiently flexible to fit a number of competing hypotheses of proximity. The algorithm employed for estimation is technically presented together with various program options. An analysis of an asymmetric brand switching matrix for automobiles is presented to illustrate the methodology. The results of this analysis are also compared with the solutions obtained from several of the currently available procedures for handling asymmetric proximity data. Finally, technical extensions to three-way analyses, hybrid models, etc., are discussed.