Decomposition Method for Changes in the Structure


  • Małgorzata Markowska Uniwersytet Ekonomiczny we Wrocławiu Wydział Ekonomii, Zarządzania i Turystyki w Jeleniej Górze Katedra Gospodarki Regionalnej
  • Andrzej Sokołowski Uniwersytet Ekonomiczny w Krakowie Wydział Zarządzania Zakład Statystyki



change decomposition, clustering structures, comparing structures, employment


Structure can be understood in two ways. The first one means the configuration of points in amultidimensional space, and the second one is a sequence of nonnegative numbers summing to one. In thepaper the authors analyse the latter meaning of structure. It is in fact an arithmetic result of comparing partswith the whole and only then can we talk about “shape”. Values of structure elements define its “size”. Weneed at least two elements to have a nontrivial structure. A change in size does not have to cause a changein shape if changes in size are proportional for all elements. The change in shape must follow the change insize. Two measures have been proposed in the paper to reflect both types of changes while comparing twostructures. They show the share of each structure element in changes and their sign define the direction ofinfluence (positive or negative). Absolute values of each measure sum up to one. As an example, the analysisof structural employment changes in the regions of Czech Republic, between 2008 and 2014 is presented inthe paper.


Download data is not yet available.


Metrics Loading ...

Author Biographies

Małgorzata Markowska, Uniwersytet Ekonomiczny we Wrocławiu Wydział Ekonomii, Zarządzania i Turystyki w Jeleniej Górze Katedra Gospodarki Regionalnej

Małgorzata Markowska, Ph.D., an associate professor at the Regional Economics Chair of Wrocław Universityof Economics. She is a member of Polish Classification Society and Polish section of Regional StudiesAssociation. Her research deals with econometric measurement, evaluation, variability and dynamics of development,competitiveness, knowledge-based economy, smart specializations, convergence and innovativenessin European regional space. As an author or co-author she has published more than 100 papers and25 chapters in books, and recently her own dissertation “Dynamic Taxonomy of Regions’ Innovativeness”.She took part in 12 projects financed by Polish National Centre of Science and European Union, and in projectsfor governmental, local administration and business units.

Andrzej Sokołowski, Uniwersytet Ekonomiczny w Krakowie Wydział Zarządzania Zakład Statystyki

Andrzej Sokolowski, Professor and the Head of Department of Statistics at the Cracow University of Economics.His academic activity is concentrated around the application of statistical methods in fields suchas economics and management, medicine, sports, politics and music. In theoretical statistics his main interestslie in mathematical statistics, multivariate analysis and medical statistics. He is an author of more than60 chapters in books and monographs, 150 papers and he has participated in 140 conferences. He was thePresident of Polish Classification Society for three terms and a member of International Federation of ClassificationSocieties Council for more than twelve years.


Chomątowski, S., Sokołowski, A. (1978). Taksonomia struktur. Przegląd Statystyczny, 2, 217–226.

Eurostat (2015, 20 października). Pozyskano z data/database[lfst_r_lfe2en2]

Kukuła, K. (1986). Przegląd wybranych miar zgodności struktur. Przegląd Statystyczny, 4, 384–401.

Regions in the European Union. Nomenclature of territorial unit for statistics NUTS 2010/EU-27 (2011). Luxembourg: European Commission.

Walesiak, M. (1983a). Podobieństwo wielkości (skali) oraz kształtu (formy) w złożonych badaniach strukturalnych. Wiadomości Statystyczne, 3, 26–28.

Walesiak, M. (1983b). Propozycja rodziny miar odległości struktur udziałowych. Wiadomości Statystyczne, 10, 23–24.



How to Cite

Markowska, M., & Sokołowski, A. (2017). Decomposition Method for Changes in the Structure. Studies of the Industrial Geography Commission of the Polish Geographical Society, 30(3), 25–32.

Most read articles by the same author(s)