A gravity-based multidimensional scaling model for deriving spatial structures underlying consumer preference/choice judgments

In multidimensional unfolding multidimensional scaling (MDS) procedures, the predicted utility of a brand for a consumer is inversely related to the distance between that consumer's ideal point and the brand position in the derived space. Most MDS models treat all brands the same regardless of their respective market share. In many product categories, however, consumer preferences are heavily influenced by the size of the existing market share (i.e., the brand mass). This article presents two versions of a new spatial methodology that incorporates the effects of brand as well as consumer mass via a spatial gravity model of consumer utility; that is, the attraction of a brand for a consumer depends not only on the distance of the brand from a consumer's ideal point but also on the current market size of the brand, as well as the consumer purchase pattern and volume. One version of the proposed model estimates brand positions and individual ideal points with two-way or three-way pick any/N binary choice data. The second version we develop provides the same spatial decomposition for two-way or three-way metric preference/dominance data. We also develop a series of nested MDS models to estimate, test, and compare four different model structures with respect to any common data set. We illustrate the proposed methodology using an actual commercial application involving physician prescription behavior and examine competing model fits.