Selecting the Optimal Multidimensional Scaling Procedure for Metric Data With R Environment
Marek Walesiak , Andrzej Dudek
AbstractIn 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.
|Journal series||Statistics in Transition. New Series, ISSN 1234-7655, e-ISSN 2450-0291, (B 15 pkt)|
|Publication size in sheets||0.95|
|Keywords in English||multidimensional scaling, normalization of variables, distance measures, HHI index, R program|
|Publication indicators||: 2017 = 0.385|
|Citation count*||18 (2020-05-24)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.