A New Multidimensional Scaling Methodology for the Representation of Inter-Product Substitutability
Advances in Consumer Research, Vol. 15 Issue 1, p 18-527, 1988
11 Pages Posted: 27 May 2016
Date Written: 1988
Batsell and Polking (1985) have recently proposed a new class of market share models. The models demonstrate that it is possible to decompose the ratios of market shares for any pair of products in any choice set into a natural hierarchy of inter-product competitive effects. One level in this hierarchy is a measure of the degree to which a product, say k, cannibalizes the market share of product i relative to product j. This paper proposes a new multidimensional scaling (MDS) methodology which uses the revealed substitutability between products to derive a representation of the competing products as points in a space of prescribed dimensionality. An interesting feature of the methodology is that it allows for the derivation of spaces which are either symmetric or asymmetric. In the symmetric space, each product is represented as a single set of coordinates. In the asymmetric space, each product is represented as 2 sets of coordinates: one set of coordinates for each product as a "drawer" of market share, and a second set of coordinates for each product as a "drawee" from which the "drawers" take share. The methodology and corresponding algorithm are discussed in detail and two applications are used to demonstrate the procedure.
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