Calculating Isotonic Regression of the Distance Function in nonmetric Multidimensional Scaling Model

Nonmetric Multidimensional Scaling model is characterized by the use of data given at least on an ordinal scale, a distance function and an isotonic transformation. Based on the concepts of Nonmetric Multidimensional Scaling and Isotonic Regressi-on of Barlow, Bartholomew, Bremmer and Brunk (1972), this paper adapts and applies the basic concepts of isotonic regression which are neccessary to calculate the disparities. It applies the Isotonic Regression to the Euclidean distance, so that the disparities are calculated as the slopes of the Greatest Convex Minorant. Although Isotonic Regression underlies the definition of the Stress given by Kruskal (1964a), the procedure presented in this work - which applies the concepts of Isotonic Regression to calculate disparities - can shed light on the definition of new goodness of fit measures in other nonmetric scaling models. unknown publishedVersion