Multidimensional Unfolding by Nonmetric Multidimensional Scaling of Spearman Distances in the Extended Permutation Polytope

Abstract

A multidimensional unfolding technique that is not prone to degenerate solutions and is based on multidimensional scaling of a complete data matrix is proposed: distance information about the unfolding data and about the distances both among judges and among objects is included in the complete matrix. The latter information is derived from the permutation polytope supplemented with the objects, called the preference sphere. In this sphere, distances are measured that are closely related to Spearman's rank correlation and that are comparable among each other so that an unconditional approach is reasonable. In two simulation studies, it is shown that the proposed technique leads to acceptable recovery of given preference structures. A major practical advantage of this unfolding technique is its relatively easy implementation in existing software for multidimensional scaling.