Grażyna Dehnel https://orcid.org/0000-0002-0072-9681 , Marek Walesiak https://orcid.org/0000-0003-0922-2323
ARTICLE

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ABSTRACT

The article describes a hybrid approach to evaluating economic efficiency of medium-sized manufacturing enterprises (employing from 50 to 249 people) in districts of Wielkopolska province, using metric and interval-valued data. The hybrid approach combines multidimensional scaling with linear ordering. In the first step, multidimensional scaling is applied to obtain a visual representation of objects in a two-dimensional space. In the next step, a set of objects is ordered linearly based on the distance from the pattern (ideal) object. This approach provides new possibilities for interpreting linearly ordered results of a set of objects. Interval-valued variables characterise the objects of interests more accurately than metric data do. Metric data are atomic, i.e. an observation of each variable is expressed as a single real number. In contrast, an observation of each interval-valued variable is expressed as an interval. The analysis was based on data prepared in a two-stage process. First, a data set of observations was obtained for metric variables describing economic efficiency of medium-sized manufacturing enterprises. These unit-level data were aggregated at district level (LAU 1) and turned into two types of data: metric and interval-valued data. In the analysis of interval-valued data, two approaches are used: symbolic-to-classic, symbolic-to-symbolic. The article describes a comparative analysis of results of the assessment of economic efficiency based on metric and interval-valued data (the results of two approaches). The calculations were made with scripts prepared in the R environment.

KEYWORDS

medium-sized enterprise, metric data, interval-valued data, multidimensional scaling, composite measures

JEL

C38, C43, C63, C88, R12

REFERENCES

BILLARD, L., DIDAY, E., (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining, John Wiley, Chichester, ISBN: 978-0-470-09016-9.

BORG, I., GROENEN, P. J. F., (2005). Modern Multidimensional Scaling. Theory and Applications. 2nd Edition, Springer Science+Business Media, New York, ISBN: 978-0387-25150-9, URL http://www.springeronline.com/0-387-25150-2.

BORG, I., GROENEN, P. J. F., MAIR, P., (2013). Applied Multidimensional Scaling, Springer, Heidelberg, New York, Dordrecht, London. ISBN 978-3-642-31847-4, URL http://dx.doi.org/10.1007/978-3-642-31848-1.

BORG, I., GROENEN, P. J. F., MAIR, P., (2018). Applied Multidimensional Scaling and Unfolding, Springer, Heidelberg, New York, Dordrecht, London. ISBN 978-3-319-73470-5, URL https://doi.org/10.1007/978-3-319-73471-2.

BORG, I., MAIR, P., (2017). The Choice of initial configurations in multidimensional scaling: local minima, fit, and interpretability, Austrian Journal of Statistics, 46 (2), pp. 19–32, URL https://doi.org/10.17713/ajs.v46i2.561.

BORYS, T., (1984), Kategoria jakości w statystycznej analizie porównawczej, Prace Naukowe Akademii Ekonomicznej we Wrocławiu, nr 284, Seria: Monografie i Opracowania nr 23, Wydawnictwo Akademii Ekonomicznej we Wrocławiu, Wrocław, ISBN: 83-7011-000-0.

BRITO, P., NOIRHOMME-FRAITURE, M., ARROYO, J., (2015). Editorial for special issue on symbolic data analysis, Advances in Data Analysis and Classification, Vol. 9, Issue 1, pp. 1–4, URL https://dx.doi.org/10.1007/s11634-015-0202-1.

CHABER, P., ŁAPIŃSKI, J., NIEĆ, M., ORŁOWSKA, J., ZAKRZEWSKI, R., WIDŁA-DOMARADZKI, Ł., DOMARADZKA, A., (2017). Raport o stanie sektora małych i średnich przedsiębiorstw w Polsce, Polska Agencja Rozwoju Przedsiębiorczości, Warszawa, URL https://badania.parp.gov.pl/raport-o-stanie-sektora-msp/stan-sektora-msp-w-polsce.

CSO, (2017). Działalność przedsiębiorstw niefinansowych w 2016 r. (Activity of Non-financial Enterprises in 2016), Central Statistical Office of Poland, Warszawa. URL http://stat.gov.pl/obszary-tematyczne/podmioty-gospodarcze-wyniki-finansowe/przedsiebiorstwa-niefinansowe/dzialalnosc-przedsiebiorstw-niefinansowych-w-2016-r-,2,12.html [Accessed 17 July 2018].

DEHNEL, G., (2015). Robust regression in monthly business survey, Statistics in Transition – new series, Vol. 16, No. 1, pp. 1–16.

EVERITT, B.S., LANDAU, S., LEESE, M., STAHL, D., (2011). Cluster Analysis, Wiley, Chichester, ISBN: 978-0-470-74991-3.

GIOIA, F., LAURO, C. N., (2006). Principal component analysis on interval data, Computational Statistics, 21 (2), pp. 343–363, URL https://doi.org/10.1007/s00180-006-0267-6.

GROENEN, P.J.F. WINSBERG, S., RODRIGUEZ, O., DIDAY, E., (2006), I-Scal: multidimensional scaling of interval dissimilarities, Computational Statistics & Data Analysis, 51 (1), pp. 360–378, URL http://dx.doi.org/10.1016/j.csda.2006.04.003.

HELLWIG, Z., (1972). Procedure of Evaluating High-Level Manpower Data and Typology of Countries by Means of the Taxonomic Method, [In:] Gostkowski Z. (ed.), Towards a system of Human Resources Indicators for Less Developed Countries, Papers Prepared for UNESCO Research Project, Ossolineum, The Polish Academy of Sciences Press, Wrocław, pp. 115–134.

HELLWIG, Z., (1981). Wielowymiarowa analiza porównawcza i jej zastosowanie w badaniach wielocechowych obiektów gospodarczych. In: Welfe, W. (ed.), Metody i modele ekonomiczno-matematyczne w doskonaleniu zarządzania gospodarką socjalistyczną, PWE, Warszawa, pp. 46–68, ISBN 83-208-0042-0.

ICHINO, M., YAGUCHI, H., (1994). Generalized Minkowski metrics for mixed feature-type data analysis, IEEE Transactions on Systems, Man, and Cybernetics, 24 (4), pp. 698–708, URL http://dx.doi.org/10.1109/21.286391.

ISARD, W., (1960). Methods of Regional Analysis: An Introduction to Regional Science. Cambridge, Massachusetts: The M.I.T. Press. 66 G. Dehnel, M. Walesiak: A comparative analysis…

JAJUGA, K., WALESIAK, M., (2000). Standardisation of Data Set under Different Measurement Scales, In: Decker, R., Gaul, W., (Eds.), Classification and Information Processing at the Turn of the Millennium, pp. 105–112, Springer-Verlag, Berlin, Heidelberg, URL http://dx.doi.org/10.1007/978-3-642-57280-7_11.

JAJUGA, K., WALESIAK, M., BĄK, A., (2003). On the General Distance Measure, in Schwaiger, M., Opitz, O., (Eds.), Exploratory Data Analysis in Empirical Research. Berlin, Heidelberg: Springer-Verlag, pp. 104–109, URL http://dx.doi.org/10.1007/978-3-642-55721-7_12.

KAPLAN, R. S., COOPER R., (1998). Cost & Effect: Using Integrated Cost Systems to Drive Profitability and Performance, Harvard Business School Press, ISBN: 978-0875847887.

KAPLAN, R. S., (2008). Conceptual foundations of the balanced scorecard. In: C. Chapman, A. Hopwood, M. Shields (Eds.), Handbook of Management Accounting Research, Vol. 3, Elsevier, ISBN: 9780080554501.

KOLIŃSKI, A., (2011). Przegląd metod i technik oceny efektywności procesu produkcyjnego, Logistyka, 5, pp. 1083–1091. MAIR, P., BORG, I., RUSCH, T., (2016), Goodness-of-fit assessment in multidimensional scaling and unfolding, Multivariate Behavioral Research, Vol. 51, No. 6, pp. 772–789, URL http://dx.doi.org/10.1080/00273171.2016.1235966.

MAIR, P., DE LEEUW, J., BORG, I., GROENEN, P. J. F., (2018). smacof: Multidimensional Scaling. R package ver. 1.10-8, URL https://CRAN.R-project.org/package=smacof.

MED, (2017). Entrepreneurship in Poland, Ministry of Economic Development, Warsaw, URL https://www.mpit.gov.pl/strony/zadania/analiza-i-ocena-polskiej-gospodarki/przedsiebiorczosc/.

R CORE TEAM, (2018). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, URL https://www.R-project.org.

WALESIAK, M., (2016). Visualization of linear ordering results for metric data with the application of multidimensional scaling, Ekonometria [Econometrics], 2 (52), pp. 9–21, URL http://dx.doi.org/10.15611/ekt.2016.2.01.

WALESIAK, M., 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, Foundation of the Cracow University of Economics, Cracow, pp. 563-572, URL http://dx.doi.org/10.14659/SEMF.2018.01.57.

WALESIAK, M., DUDEK, A., (2017). Selecting the optimal multidimensional scaling procedure for metric data with R environment, Statistics in Transition – new series, 18 (3), pp. 521–540, URL http://dx.doi.org/10.21307/stattrans-2016-084.

WALESIAK, M., DUDEK, A., (2018a). clusterSim: Searching for Optimal Clustering Procedure for a Data Set. R package, version 0.47-2, URL https://CRAN.R-project.org/package=clusterSim.

WALESIAK, M., DUDEK, A., (2018b). mdsOpt: Searching for Optimal MDS Procedure for Metric and Interval-valued Symbolic Data, R package, version 0.3-2, URL https://CRAN.R-project.org/package=mdsOpt.

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