Flexible Multidimensional Scaling for Human Smart Development Analysis in EU Countries

Malgorzata Markowska, Andrzej Sokolowski, Danuta Strahl
European Research Studies Journal, Volume XXIV, Special Issue 4, 435-445, 2021
DOI: 10.35808/ersj/2728


Purpose: The aim of the paper is to propose a flexible procedure to Multidimensional Scaling, allowing to calculate the input distance matrix based on slightly different set of variables for each pair of objects. Design/Methodology/Approach: The procedure starts from the classical standardization of each variable. Before the calculation of flexible distance between two objects, we eliminate the variable with the biggest absolute value in the first object, and the same we do for the second object. So, we have two variables less in the list for these two objects. If by chance the same variable is pointed for elimination by both objects, the next variable with the biggest (out of both objects) absolute standardized value should be eliminated. With this procedure, each element of distance matrix is based on the same number of variables, but some of actual variables can be different. Findings: As an example – Flexible Multidimensional Scaling is performed on the list of 17 variables describing so called smart society, for 28 European Union countries. It shows how the proposed procedure works in practice. Practical Implications: The proposed flexible procedure can be used for the analysis of any problem treated by Multidimensional Scaling. Originality/Value: Flexible Multidimensional Scaling (FMDS) is a new idea and method. It eliminates some elements of subjective choice of initial variables and seems to be more robust against outliers than classical Multidimensional Scaling (MDS).

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