Multidimensional scaling is a family of procedures that aim at producing a low-dimensional representation of object similarity/dissimilarity. Consider n brands and a similarity matrix, whose entry dij measures the distance between brands i and j, as perceived by consumers. This matrix is a direct input of multidimensional scaling, whereas other methods aim at computing distances. Then, we want to find a representation of brands as points on a plane, in such a way that the geometric (Euclidean) distance δij between points is approximately proportional to the perceived distance between brands:
for some irrelevant constant α. The idea is illustrated in Fig. 15.5. In a marketing context, for instance, multidimensional scaling can help researchers to understand how consumers perceive brands and how product features relate to each other. We observe that multidimensional scaling procedures accomplish a form of dimensionality reduction, are exploratory in nature, and can be classified as interdependence methods.
Table 15.2 Correspondence analysis works on a two-way contingency table.
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