Solving degeneracy and stability in nonmetric unfolding

Nonmetric unfolding is a powerful (nonparametric) analytical tool generating a preference-based joint display of subjects (e.g., consumers) and objects (e.g., brands or products). Unfortunately, nonmetric unfolding frequently produces degenerate unfolding solutions (i.e., unfolding solutions showing close-to-perfect model fit irrespective of the data analyzed). Moreover, there are no methods to assess the quality of the unfolding solution in terms of stability and accuracy. In this paper, we resolve these important issues simultaneously by using a bootstrapped penalized nonmetric unfolding approach. In line with the explorative and visual nature of nonmetric unfolding, we introduce methods for visualizing the stability of unfolding solutions. In addition, we propose numerical measures for stability and validity of nonmetric unfolding solutions that can be used to identify accurate, nondegenerate and stable solutions. Finally, for large scale data, as often encountered in marketing, we propose a greedy search algorithm. We illustrate our methodology using three applications in the food domain.

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