On evaluating the equivalency of alternative MDS representations

Abstract

A typical question in MDS is whether two alternative configurations that are both acceptable in terms of data fit may be considered “practically the same”. To answer such questions on the equivalency of MDS solutions. Lingoes & Borg (1983) have recently proposed a quasistatistical decision strategy that allows one to take various features of the situation into account. This paper adds another important piece of information to this approach: for the Lingoes-Borg decision criterion R , we compute what proportion of R -values is greater/less than the observed coefficient if one were to consider all possible alternative distance sets within certain bounds defined by the observed fit coefficients for two alternative MDS solutions, what are the limits of acceptability for such fit coefficients, and how are the observed MDS configurations interrelated.