A Quasi-Metric Approach to Multidimensional Unfolding for Reducing the Occurrence of Degenerate Solutions

Abstract

In multidimensional unfolding (MDU), one typically deals with two-way, two-mode dominance data in estimating a joint space representation of row and column objects in a derived Euclidean space. Unfortunately, most unfolding procedures, especially nonmetric ones, are prone to yielding degenerate solutions where the two sets of points (row and column objects) are disjointed or separated in the derived joint space, providing very little insight as to the structure of the input data. We present a new approach to multidimensional unfolding which reduces the occurrence of degenerate solutions. We first describe the technical details of the proposed method. We then conduct a Monte Carlo simulation to demonstrate the superior performance of the proposed model compared to two non-metric procedures, namely, ALSCAL and KYST. Finally, we evaluate the performance of alternative models in two applications. The first application deals with student rank-order preferences (nonmetric data) for attending various graduate business (MBA) programs. Here, we compare the performance of our model with those of KYST and ALSCAL. The second application concerns student preference ratings (metric data) for a number of popular brands of analgesics. Here, we compare the performance of the proposed model with those of two metric procedures, namely, SMACOF-3 and GENFOLD 3. Finally, we provide some directions for future research.