Selecting the optimal multidimensional scaling procedure for metric data with R environment

Abstract

In multidimensional scaling (MDS) carried out on the basis of a metric data matrix (interval, ratio), the main decision problems relate to the selection of the method of normalization of the values of the variables, the selection of distance measure and the selection of MDS model. The article proposes a solution that allows choosing the optimal multidimensional scaling procedure according to the normalization methods, distance measures and MDS model applied. The study includes 18 normalization methods, 5 distance measures and 3 types of MDS models (ratio, interval and spline). It uses two criteria for selecting the optimal multidimensional scaling procedure: Kruskal’s Stress-1 fit measure and Hirschman-Herfindahl HHI index calculated based on Stress per point values. The results are illustrated by an empirical example.