Comparative Analysis of the Ordering of Polish Provinces in Terms of Social Cohesion

Grażyna Dehnel, Marek Walesiak, Marek Obrębalski


The article describes an assessment of the social cohesion of Polish provinces. The assessment was based on classical metric and interval-valued data using a hybrid approach combining multidimensional scaling with linear ordering. In the first step, after applying multidimensional scaling, the objects of interest were represented in a two-dimensional space. In the second step, the objects were linearly ordered based on the Euclidean distance from the pattern object. Interval-valued variables characterize the objects of interests more accurately than do metric data. Classic data are of an atomic nature, i.e. an observation of each variable is expressed as a single real number. By contrast, an observation of each interval-valued variable is expressed as an interval. Interval-valued data were derived by aggregating classic metric data on social cohesion at the level of districts to the province level. The article describes a comparative analysis of the results of an assessment of the social cohesion of Polish provinces based on classical metric data and interval-valued data.


social cohesion, composite indicators, interval-valued data, multidimensional scaling, R software

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Annoni, P. and Dijkstra, L. (2016) The EU Regional Social Progress Index: Methodological Note. Brussels: European Commission.

Balcerzak, A. P. (2015) “Wielowymiarowa analiza spójności społecznej w krajach Unii Europejskiej w kontekście strategii Europa 2020” in B. Bartniczak and K. Trzeciak (eds) Aktualne trendy w zarządzaniu środowiskiem. Jelenia Góra: Wydawnictwo AD REM.

Billard, L. and Diday, E. (2006) Symbolic Data Analysis: Conceptual Statistics and Data Mining. Chichester: John Wiley.

Borg, I. and Groenen, P. J. F. (2005) Modern Multidimensional Scaling: Theory and Applications. New York: Springer Science+Business Media.

Bottoni, G. (2018) “A Multilevel Measurement Model of Social Cohesion”. Social Indicators Research 136 (3): 835–57,

Concerted Development of Social Cohesion Indicators: Methodological Guide (2005) Strasbourg: Council of Europe Publishing.

Dickes, P. and Valentova, M. (2013) “Construction, Validation and Application of the Measurement of Social Cohesion in 47 European Countries and Regions”. Social Indicators Research 113 (3): 827–46,

Dickes, P., Valentova, M. and Borsenberger, M. (2010) “Construct Validation and Application of a Common Measure of Social Cohesion in 33 European Countries”. Social Indicators Research 98 (3): 451–73,

Everitt, B.S., Landau, S., Leese, M. and Stahl, D. (2011) Cluster Analysis. Chichester: Wiley.

Hellwig, Z. (1972) “Procedure of Evaluating High-level Manpower Data and Typology of Countries by Means of the Taxonomic Method” in Z. Gostkowski (ed.) Towards a System of Human Resources Indicators for Less Developed Countries: Papers Prepared for UNESCO Research Project. Wrocław: Ossolineum, The Polish Academy of Sciences Press.

Hellwig, Z. (1981) “Wielowymiarowa analiza porównawcza i jej zastosowanie w badaniach wielocechowych obiektów gospodarczych” in W. Welfe (ed.) Metody i modele ekonomiczno-matematyczne w doskonaleniu zarządzania gospodarką socjalistyczną. Warszawa: PWE.

Ichino, M. and Yaguchi, H. (1994) “Generalized Minkowski Metrics for Mixed Feature-type Data Analysis”. IEEE Transactions on Systems, Man, and Cybernetics 24 (4): 698708,

Jajuga, K., Walesiak, M. and Bąk, A. (2003) “On the General Distance Measure” in M. Schwaiger and O. Opitz (eds) Exploratory Data Analysis in Empirical Research. Berlin–Heidelberg: Springer-Verlag.

Mair, P., De Leeuw, J., Borg, I. and Groenen, P. J. F. (2018) smacof: Multidimensional Scaling. R package, version 1.10-8,

My Region, My Europe, Our Future: Seventh Report on Economic, Social and Territorial Cohesion (2017). Brussels: European Commission.

Rajulton, F., Ravanera, Z. R. and Beaujot, R. (2007) “Measuring Social Cohesion: An Experiment Using the Canadian National Survey of Giving, Volunteering, and Participating”. Social Indicators Research 80 (3): 461–92,

R Core Team (2018) R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria,

Walesiak, M. (2016) “Visualization of Linear Ordering Results for Metric Data with the Application of Multidimensional Scaling”. Ekonometria 2 (52): 9–21,

Walesiak, M. and Dudek, A. (2017) “Selecting the Optimal Multidimensional Scaling Procedure for Metric Data with R Environment”. Statistics in Transition: New Series 18 (3): 521–40,

Walesiak, M. and Dudek, A. (2018a) clusterSim: Searching for Optimal Clustering Procedure for a Data Set. R package, version 0.47-2,

Walesiak, M. and Dudek, A. (2018b) mdsOpt: Searching for Optimal MDS Procedure for Metric and Interval-valued Symbolic Data. R package, version 0.3-2,

Walesiak, M. and Dehnel, G. (2018) “Evaluation of Economic Efficiency of Small Manufacturing Enterprises in Districts of Wielkopolska Province Using Interval-valued Symbolic Data and the Hybrid Approach” in M. Papież and S. Śmiech (eds) The 12th Professor Aleksander Zeliaś International Conference on Modelling and Forecasting of Socio-economic Phenomena. Conference Proceedings. Cracow: Foundation of the Cracow University of Economics.