Hoffman, Donna L., Peter G.M. van der Heijden, and Thomas P. Novak, "Mapping Asymmetry in Categorical Consumer Choice Data," (December 2001).
Abstract. Marketers are often interested in graphically depicting the patterns of consumer choice behavior. In such situations, square asymmetric frequency data arise commonly. We show how to graphically model components of asymmetry in these categorical data applications. Our approach considers asymmetry in terms of its component departures from the overall or total structure in the asymmetric frequency matrix.
Two residual maps are developed which represent distinct sources of asymmetry in brand choice: share driven asymmetry and share-adjusted asymmetry. Thus, the maps show deviations from symmetry due to changes in market shares and consumer heterogeneity. We formulate the problem in the context of loglinear modeling and the singular value decomposition (SVD) of residual matrices. The components of asymmetric structure (residuals from the models) are decomposed via the SVD and represented graphically in a low-dimensional space. We illustrate the method, easily implementable using standard statistical packages, with two examples of automobile choice. One is the well known 16-by-16 car trade-in problem from Harshman, Green, Wind, and Lundy (1982), and the other is a more recent example drawn from the Colombo, Ehrenberg and Sabavala (1994) "car challenge." Download pdf.
