Aproksymacja wyników dynamicznego skalowania wielowymiarowego trendami nieliniowymi
Nonlinear trend approximation of the results of dynamic Multidimensional Scaling

Summary/Abstract: The main idea of Multidimensional Scaling is the positioning of objects on the plane in such a way that distances on that plane reflect the distances calculated in the original classification space. Most goodness-of-fit measures are based on the sum of squares of differences between the original and 2D matrix, and the most popular measure is STRESS introduced by Kruskal [1964]. In dynamic multidimensional scaling we propose a procedure which takes into account not only the relations between different objects, but also relations of an object with itself at different time points. Data cube should be transformed into spatio-temporal data matrix which is subject to global standardization. The results can be presented on a plane but also in 3D space with one dimension devoted to time variable. We propose to approximate trajectories with polynomial trend functions. The analysis of 28 European Union countries characterized by 5 macroeconomic variables, in 2004-2015 serves as an illustrative example.

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