Using Symbolic Data In Gravity Model Of Population Migration To Reduce Modifiable Areal Unit Problem (Maup)

• Authors: Wilk Justyna

Abstracts

EN

Spatial analyses suffer from modifiable areal unit problem (MAUP). This occurs while operating on aggregated data determined for high-level territorial units, e.g. official statistics for countries. Generalization process deprives the data of variation. Carrying out research excluding territorial distribution of a phenomenon affects the analysis results and reduces their reliability. The paper proposes to use symbolic data analysis (SDA) to reduce MAUP. SDA proposes an alternative form of individual data aggregation and deals with multivariate analysis of interval-valued, multi-valued and histogram data. The paper discusses the scale effect of MAUP which occurs in a gravity model of population migrations and shows how SDA can deal with this problem. Symbolic interval-valued data was used to determine the economic distance between regions which served as a separation function in the model. The proposed approach revealed that economic disparities in Poland are lower than official statistics show but they are still one of the most important factors of domestic migration flows.

Keywords

EN

modifiable areal unit problem (MAUP); symbolic data analysis (SDA); gravity model; population migration; economic distance

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2015
• Volume: 16
• Issue: 2
• Pages: 243-264

Contributors

author

Wilk Justyna

• Wrocław University of Economics, Department of Econometrics and Computer Science, 58-500 Jelenia Góra (Poland), Nowowiejska 3 Street

References

• ANDERSON, J. E., (1979). A Theoretical Foundation for the Gravity Model, American Economic Review, 69 (1), pp. 106−116.
• ANSELIN, L., (1988). Spatial Econometrics: Methods and Models, Kluwer Academic, Dordrecht.
• ARBIA, G., (1989). Spatial Data Configuration in Statistical Analysis of Regional Economic and Related Problems, Advanced Studies in Theoretical and Applied Econometrics, Vol. 14, Kluwer Academic Publishers, Dordrecht-Boston-London.
• BEINE, M., BERTOLI, S., FERNÁNDEZ-HUERTAS MORAGA, J., (2015). A Practitioners’ Guide to Gravity Models of International Migration, World Economy.
• BENALI, H., ESCOFIER, B., (1990). Analyse factorielle lissée et analyse factorielle des différences locales, Revue de statistiques appliquées, XXXVIII (2), pp. 55−76.
• BERTOLI, S., FERNÁNDEZ-HUERTAS MORAGA, J., (2013). Multilateral resistance to migration, Journal of Development Economics, 102, May, pp. 79−100.
• BILLARD, L., DIDAY, E., (2006). Symbolic Data Analysis. Conceptual Statistics and Data Mining, Wiley, Chichester.
• BOCK, H.-H., DIDAY, E. (Eds.), (2000). Analysis of symbolic data. Exploratory methods for extracting statistical information from complex data, Springer-Verlag, Berlin-Heidelberg.
• BUNEA, D., (2012). Modern Gravity Models of Internal Migration. The Case of Romania, Theoretical and Applied Economics, Vol. XIX, No. 4(569), pp. 127−144.
• CHOJNICKI, Z., (1966). Application of gravity and potential models in spatio-economic research (in polish), PWN, Warsaw.
• CHOJNICKI, Z., CZYŻ, T., RATAJCZAK, W., (2011). Potential model. Theoretical basis and applications in spatio-economic and regional research (in polish), Bogucki Wydawnictwo Naukowe, Poznan.
• CLIFF, A. D., ORD, J. K., (1981). Spatial processes: models and applications, Pion, London.
• CONLEY, T. G., TOPA, G., (2002). Socio-economic distance and spatial patterns in unemployment, Journal of Applied Econometrics, Vol. 17/4.
• DARK, S. J., BRAM, D., (2007). The modifiable areal unit problem (MAUP) in physical geography, “Progress in Physical Geography”, Vol. 31, No. 5.
• DIDAY, E., NOIRHOMME-FRAITURE, M. (Eds.), (2008). Symbolic data analysis and the Sodas software, John Wiley & Sons, Chichester.
• DUDEK, A., PEŁKA, M., WILK, J., (2013). symbolicDA package of R-CRAN, http://cran.r-project.org/web/packages/symbolicDA/index.html.
• FISCHER, M. M., WANG, J., (2011). Spatial data analysis: models, methods and techniques, Springer Briefs in Regional Science, Springer, Berlin.
• FOTHERINGHAM, A. S., CHARLTON, M.E., BRUNSDON, C. F., (2001). Spatial Variations in School Performance: a Local Analysis Using Geographically Weighted Regression, Geographical & Environmental Modelling, Vol. 5, pp. 43−66.
• FOTHERINGHAM, A. S., O’KELLY, M. E., (1989). Spatial interaction models: formulations and applications, Kluwer, Dordrecht,
• GATNAR, E., WALESIAK, M. (Ed.), (2011). Qualitative and symbolic data analysis using R program (in polish), C.H. Beck, Warsaw.
• GEHLKE, C. E., BIEHL, K., (1934). Certain effects of grouping upon the size of the correlation coefficient in census tract material, Journal of the American Statistical Association, No. 29.
• GHATAK, S., MULHERN, A., WATSON, J., (2008). Inter-regional migration in transition economies. The case of Poland, Review of Development Economics, No. 12(1), Oxford, pp. 209−222.
• GOTWAY CRAWFORD, C. A., YOUNG, L. J., (2004). A spatial view of the ecological inference problem, In: G. King, O. Rosen, M. Tanner (Eds.), Ecological Inference: New Methodological Strategies, Cambrige University Press, pp. 233−244.
• GRABIŃSKI, T., MALINA, A., WYDYMUS, S., ZELIAŚ, A., (1988). International statistics methods (in polish), PWE, Warsaw.
• GREENWOOD, M. J., (1997). Internal migration in developed countries, In: Rosenzweig, M. R. and Stark, O. (Eds.), Handbook of Population and Family Economics, vol. 1B, Elsevier, Amsterdam, pp. 648−720.
• GRIFFITH, D. A., FISCHER, M., (2013). Constrained variants of the gravity model and spatial dependence: Model specification and estimation issues, Journal of Geographical Systems, 15(3), pp. 291−317.
• HOLZER, J. Z., (2003). Demography (in polish), PWE, Warsaw.
• HORNING, A., DZIADEK S., (1987). Outline of land transport geography (in polish), PWN.
• ICHINO, M., YAGUCHI, H., (1994). Generalized Minkowski Metrics for Mixed Feature-Type Data Analysis, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 24, No. 4.
• ISARD, W., (1960). Methods of regional analysis, MIT Press, Cambridge.
• JELINSKI, D. E., WU, J., (1996). The modifiable areal unit problem and implications for landscape ecology, Landscape Ecology, Vol. 11, No. 3, pp. 129−140
• KING, G., (1997). A solution to the ecological inference problem: reconstructing individual behaviour from aggregate data, Princeton University Press, Princeton.
• KING, G., TANNER M. A., ROSEN O. (Eds.), (2004). Ecological Inference: New Methodological Strategies, Cambridge University Press, New York.
• KAPISZEWSKI, M., DURHAM, H., REES, P., (1999). Internal Migration and Regional Population Dynamics In Europe: Poland Case Study, In: P. Rees, M. Kupiszewski (Eds.), Internal Migration and Regional Population Dynamics in Europe: A Synthesis, Collection Demography, Council of Europe, Strasbourg.
• LESAGE, J. P., PACE, R. K., (2008). Spatial econometric modeling of origin-destination flows, Journal of Regional Science, Vol. 48, No. 5, pp. 941−968.
• Local Data Bank of the Central Statistical Office of Poland, http://www.stat.gov.pl/bdl.
• LUCAS, R., (1997). Internal Migration in Developing Countries, In: M.R. Rosenzweig, O. Stark (Eds.), Handbook of Population and Family Economics, Elsevier Science B.V, Amsterdam, pp. 721−798.
• MOELLERING, H., TOBLER, W. R., (1972). Geographical variances, Geographical Analysis, Vol. 4, pp. 34−50.
• OPENSHAW, S., TAYLOR, P. J., (1979). A million or so correlation coefficients: three experiments on the modifiable areal unit problem, In: N. Wringley (Ed.), Statistical Applications in the spatial sciences, Pion, London, pp. 127−144.
• OPENSHAW, S., (1984). The Modifiable Areal Unit Problem, GeoBooks, CATMOG 38, Norwich.
• PARIKH, A., VAN LEUVENSTEIJN, M., (2002). Internal migration in regions of Germany: A panel data analysis, Working Paper, No. 12, European Network of Economic Policy Research Institutes.
• PIETRZAK, M., ŻUREK, M., MATUSIK, S., WILK, J., (2012). Application of Structural Equation Modeling for analysing internal migration phenomena in Poland, Przegląd Statystyczny (Statistical Review), No 4, Vol. LIX, pp. 487−503.
• PIETRZAK, M. B., DRZEWOSZEWSKA, N., WILK, J., (2012). The analysis of interregional migrations in Poland in the period of 2004-2010 using panel gravity model, Dynamic Econometric Models, Vol. 12(2012), pp. 111−122.
• PIETRZAK, M., WILK, J., (2014). The economic distance in spatial phenomena modelling with the use of gravity model (in polish), In: K. Jajuga, M. Walesiak (red.), Taksonomia 22. Klasyfikacja i analiza danych – teoria i zastosowania, Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu, 37, pp. 177−185.
• Reshaping Economic Geography, (2009). World Bank, Washington.
• ROY, J. R., (2004). Spatial Interaction Modeling: A Regional Science Context, Springer-Verlag, Berlin.
• SANTOS SILVA, J., TENREYRO, S., (2006). The log of gravity, The Review of Economics and Statistics, 88, pp. 641−58.
• SEN, A., SMITH, T. E., (1995). Gravity models of spatial interaction behavior, Springer, Berlin-Heilderberg-New York.
• SHEPHERD, B., (2013). The Gravity Model of International Trade: A User Guide, United Nations ESCAP & ARTNET.
• SUCHECKA, J. (Ed.), (2014). Spatial statistics. Spatial structures analysis methods (in polish), C.H. Beck., Warsaw.
• SUCHECKI, B. (Ed.), (2010). Spatial econometrics. Spatial data analysis methods and models (in polish), C.H. Beck, Warsaw.
• TATE, N. J., ATKINSON, P. M. (Eds.), (2001). Modelling scale in geographical information sciences, Wiley & Sons, London.
• TOBLER, W., (1979). Smooth pycnophylactic interpolation for geographical regions, Journal of the American Statistical Association, Vol. 74, pp. 519−536.
• TOBLER, W., (1989). Frame independent spatial analysis, In: Accuracy of Spatial Databases, M. Goodchild S. Gopal (Eds.), CRC Press, pp.115−122.
• TODARO, M., (1980). Internal Migration in Developing Countries. A survey, In: R. A. Easterlin, Population and Economic Change in Developing Countries, University of Chicago Press, Chicago, pp. 361−402.
• VAN DER GAAG, N. (Ed.), (2003). Study of past and future interregional migration trends and patterns within European Union countries: in search of a generally applicable explanatory model, Report on behalf of Eurostat.
• WHITE, M. J., LINDSTROM, D. P., (2006). Internal Migration, In: D.L. Poston, M. Micklin (Eds.), Handbook of Population, Springer, Berlin-Heilderberg.
• WILK, J., (2012). Symbolic approach in regional analyses, Statistics in Transition – new series, Vol. 13, No 3, December 2012, pp. 581−600, http://stat.gov.pl/cps/rde/xbcr/pts/SIT_13_3_December_2012.pdf.
• WILK, J., (2011). Cluster analysis based on symbolic data (In Polish), In: E. Gatnar, M. Walesiak (Eds.), Analiza danych jakościowych i symbolicznych z wykorzystaniem programu R, C.H. Beck, Warsaw, pp. 262−279.
• WILK, J., (2006). Problems of symbolic objects classification. Symbolic distance measures (In Polish), In: J. Garczarczyk (Ed.), Ilościowe i jakościowe metody badania rynku. Pomiar i jego skuteczność, Zeszyty Naukowe Akademii Ekonomicznej w Poznaniu, 71, pp. 69−83.
• WONG, D., The modifiable areal unit problem (MAUP), (2009). In: Fotheringham A.S., Rogerson P.A. (Eds.), The SAGE Handbook of Spatial Analysis, SAGE Publications Ltd., pp. 105−123.
• YULE, U., KENDALL M. S., (1950). An introduction to the theory of statistics, Charles Griffin, London.
• ZELIAŚ, A. (Ed.), (1991). Spatial econometrics (In Polish), PWE, Warsaw.