SELECTING THE OPTIMAL MULTIDIMENSIONAL SCALING PROCEDURE FOR METRIC DATA WITH R ENVIRONMENT

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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics , Statistics & Probability

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ISSN: 1234-7655
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VOLUME 18 , ISSUE 3 (September 2017) > List of articles

SELECTING THE OPTIMAL MULTIDIMENSIONAL SCALING PROCEDURE FOR METRIC DATA WITH R ENVIRONMENT

Marek Walesiak / Andrzej Dudek

Keywords : multidimensional scaling, normalization of variables, distance measures, HHI index, R program

Citation Information : Statistics in Transition New Series. Volume 18, Issue 3, Pages 521-540, DOI: https://doi.org/10.21307/stattrans-2016-084

License : (CC BY 4.0)

Published Online: 20-November-2017

Open Access article funded by Polish National Science Centre, decision DEC-2015/17/B/HS4/00905

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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.

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