Abstract
This work contains a description of a technique for constructing two synthetic indicators (measures) using a graphical presentation in the form of radar maps. The paper presents the structure and properties of indicators and their formal notation specially created for this purpose using the analogon of a scalar product of vectors. In particular, it proves the theorem on polygon fields, induced by radar maps, prepared for structural vectors, which allows to build concentration indicators. In order to demonstrate the usefulness of tools constructed by such means, the example shows how significant structural changes can be imperceptible when utilizing only the GINI concentration indicator’s value, but are noticeable when using the concentration indicator developed by the authors. In addition, it illustrates the change in the value of concentration indicators (GINI and the indicator developed by the authors) on two families of Lorenz curves, together with changes in concentration. The practical application of this technique for constructing indicators that create rankings is presented on empirical data on the level of material deprivation in the countries that joined the EU in 2004 and 2007. These data have also been annotated (for comparison purposes) using the so-called overrepresentation maps (Grade Correspondence Analysis method).
Highlights
The graphical presentation of data plays a very important role in the Multidimensional Data Analysis
The Z0, . . . , Z3 structures are illustrated in Figure 2: on the left as Lorenz curves, and on the right they were presented as radar charts
It illustrates how significant changes may be unnoticeable for the GINI indicator, but will be noted when we apply two GINI i and GR indices for the analysis
Summary
The graphical presentation of data plays a very important role in the Multidimensional Data Analysis. These curves are the diagonal of the unit square and the Lorenz curve (see in [1]) Both of these, synthetic index W and GINI measures, are used as tools for multidimensional comparative analysis, based on graphs of objects in the Cartesian system. An analogon of the scalar product of vectors (under the name S-scalar product) and the vector norm (under the name S-norm) has been introduced These concepts were used to formally present the technique of creating and study properties of indicators (using the idea of presentation in the form of radar charts). We performed a similar analysis of empirical material using overrepresentation maps in order to compare the two methods
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