Redefining the Modifiable Areal Unit Problem Within Spatial Econometrics, the Case of the Aggregation Problem
DOI:
https://doi.org/10.12775/EQUIL.2014.021Keywords:
spatial econometrics, modifiable areal unit problem, scale problem, aggregation problemAbstract
The paper focuses on the issue of the aggregation problem, which is frequently discussed within spatial econometrics. The aggregation problem is one of the two aspects of the modifiable areal unit problem (MAUP). The aggregation problem is connected with the volatility of the obtained results occurred when various compositions of territorial units for the same aggregation scale were applied. The objective of the present paper is to consider the redefinition of aggregation problem and showing positive solution of the aggregation problem based on the empirical example of determining agricultural macroregions. In the article the aggregation problem was defined as a problem of establishing a particular composition of territorial units at a selected aggregation scale in a such a way that is remains in the quasi composition of regions within the undertaken research problem. The paper also presented the procedure for determining agricultural macroregions where the analysis of the spatial volatility of the agrarian structure and the current knowledge on the agriculture in Poland were applied. In addition, the paper considered the final areal interpretation problem connected with the incorrect determination of the area in relation to which final conclusions are drawn. The problem was presented basing on the example of the establishment of the average concentration of the area of agricultural land in Poland with the use of the Gini index calculated for districts. The paper emphasised that ignoring the final areal interpretation problem in spatial analyses may lead to an apparent identification of the modifiable areal unit problem.
Downloads
Download data is not yet available.
References
Anselin L. (1988), Spatial Econometrics: Method and Models, Kluwer Academic Publishers, Netherlands.
Arbia G. (1989), Spatial Data Configuration in Statistical Analysis of Regional Economics and Related Problems, Kluwer Academic Publisher, Dordrecht.
Arbia G. (2006), Spatial Econometrics, Statistical Foundations and Applications to Regional Convergence, Springer-Verlag, Berlin Heidelberg.
Blalock H. (1964), Causal inferences in nonexperimental research, University of North Carolina Press, Chapel Hill.
Bukraba-Rylska I. (2008), Socjologia wsi polskiej, PWN, Warszawa.
Ceriani L., Verme P. (2011), The origins of the Gini index: extracts from Variabilit? e Mutabilit? (1912) by Corrado Gini, ?Journal of Economic Inequality?, Vol. 10, http://dx.doi.org/10.1007/s10888-011-9188-x.
Flowerdew R. (2011), How serious is the Modifiable Areal Unit Problem for analysis of English census data?, ?Population Trends?, No 145, http://dx.doi.org/10.1057/pt.2011.20.
Goraj L., Cholewa I., Osuch D., Płonka R. (2010), Analiza skutków zmian we Wspólnotowej Typologii Gospodarstw Rolnych, Instytut Instytut Ekonomiki Rolnictwa i Gospodarki Żywnościowej - Państwowy Instytut Badawczy, Warszawa.
Holt D., Steel D.G., Tranmer M. (1996), Area homogeneity and the modifiable areal unit problem, ?Geographical Systems?, Vol. 3.
Fotheringharn, A.S., Wong D.W.S. (1991), The modifiable area unit problem in multivariate analysis, ?Environment und Planning A?, Vol. 23.
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?, Vol. 29, http://dx.doi.org/10.2307/2277827.
Manley D., Flowerdew R., Steel D. (2006), Scales, levels and processes: Studying spatial patterns of British census variables Computers, ?Environment and Urban Systems?, Vol. 30.
Marble D.F. (2000), Some thoughts on the integration of spatial analysis and Geographic Information Systems, ?Journal of Geographical Systems?, Vol. 2, http://dx.doi.org/10.1007/s101090050026.
Michna W. (2005), Zróżnicowanie funkcji gospodarstw rolnych w ujęciu przestrzennym, Instytut Ekonomiki Rolnictwa i Gospodarki Żywnościowej ? Państwowy Instytut Badawczy, Warszawa.
Openshaw S. (1977a), A geographical solution to scale and aggregation problems in region-building, partitioning and spatial modelling, ?Transactions of the Institute of British Geographers?, New Series, Vol. 2, http://dx.doi.org/10.2307/622300.
Openshaw S. (1977b), Algorithm 3: a procedure to generate pseudo-random aggregationsof N zones into M zones, where M is less than N', ?Environment and Planning A?, Vol. 9.
Openshaw S. (1977c), Optimal zoning systems for spatial interaction models, ?Environment and Planning A?, Vol. 9, http://dx.doi.org/10.1068/a090169.
Openshaw S., Taylor P.J. (1979), A million or so correlation coefficients: three experiments on the modifiable areal unit problem, [in:] Wrigley N. (ed.), Statistical methods in the spatial sciences, London: Pion.
Openshaw S. (1984a), The Modifiable Areal Unit Problem, GeoBooks, CATMOG 38, Norwich.
Openshaw S. (1984b), Ecological fallacies and the analysis of areal census data, ?Environment and Planning A?, Vol. 16, http://dx.doi.org/10.1068/a160017.
Paelinck J.H.P. (2000), On aggregation in spatial econometric modelling, ?Journal of Geographical Systems?,Vol. 2, http://dx.doi.org/10.1007/PL00011452 .
Pietrzak M. B. (2010a), Analiza danych przestrzennych a jakość informacji, [in:] Trzaskalik T. (ed.), Modelowanie preferencji a ryzyko '09, Wydawnictwo Uniwersytetu Ekonomicznego, Katowice.
Pietrzak M. B. (2010b), Problem identyfikacji struktury danych przestrzennych, ?Acta Universitatis Nicolai Copernici Ekonomia?, XLI, z. 397, s. 83-98.
Pietrzak M. B. (2013), Interpretation of Structural Parameters for Models with Spatial Autoregression, ?Equilibrium? Vol. 8 I. 2,, s. 129-155, http://dx.doi.org/ 10.12775/EQUIL.2013.010 .
Pietrzak M. B., (2014a), Redefining the modifiable areal unit problem within spatial econometrics, the case of the scale problem, ?Equilibrium? Volume 9, Issue 2 (forthcoming).
Pietrzak M. B. (2014b), The modifiable areal unit problem - analysis of correlation and regression, ?Equilibrium?, Volume 9, Issue 4 (forthcoming).
Pietrzak M.B, Wilk J,. Kossowski T., Bivand R. (2014), The identification of spatial dependence in the analysis of regional economic development - join-count test application, [in:] Papież M. & Śmiech S. (ed.), Proceedings of 8th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, Cracow: Foundation of the Cracow University of Economics (forthcoming).
Reynolds H. D. (1998), The Modifiable Area Unit Problem: Empirical Analysis by Statistical Simulation, doctoral thesis, graduate Deparment of Geography, University of Toronto.
Roberts K.D. (1982), Agrarian structure and labor mobility in rural Mexico, ?Population and Development Review?, Vol. 8, http://dx.doi.org/10.2307/1972988.
Robinson W.S. (1950), Ecological Correlations and the Behavior of Individuals, ?American Sociological Review?, Vol. 15, No. 3, http://dx.doi.org/10.2307/2087176.
Skarżyńska A., Goraj L., Ziętek I. (2005), Metodologia SGM ?2002? dla typologii gospodarstw rolnych w Polsce, Instytut Instytut Ekonomiki Rolnictwa i Gospodarki Żywnościowej - Państwowy Instytut Badawczy, Warszawa.
Suchecki B. (ed.) (2010), Ekonometria Przestrzenna. Metody i modele analizy danych przestrzennych, Wydawnictwo C.H.Beck, Warszawa.
Szulc E. (2007), Ekonometryczna analiza wielowymiarowych procesów gospodarczych, Wydawnictwo UMK, Toruń.
Tate N., Atkinson P.M. (ed.) (2001), Modelling scale in geographical information science, John Wiley & Sons, Chichester.
Tranmer M., Steel D. (2001), Using Local Census Data to Investigate Scale Effects [in:] Tate N., Atkinson P. (ed.), Modelling scale in geographical information science, Chichester: John Wiley & Sons.
Woś A. (ed.) (1998), Encyklopedia agrobiznesu, Fundacja Innowacja, Warszawa.
Yule G.U., Kendall M.G. (1950), An introduction to the theory of statistics, Griffin, London.
Arbia G. (1989), Spatial Data Configuration in Statistical Analysis of Regional Economics and Related Problems, Kluwer Academic Publisher, Dordrecht.
Arbia G. (2006), Spatial Econometrics, Statistical Foundations and Applications to Regional Convergence, Springer-Verlag, Berlin Heidelberg.
Blalock H. (1964), Causal inferences in nonexperimental research, University of North Carolina Press, Chapel Hill.
Bukraba-Rylska I. (2008), Socjologia wsi polskiej, PWN, Warszawa.
Ceriani L., Verme P. (2011), The origins of the Gini index: extracts from Variabilit? e Mutabilit? (1912) by Corrado Gini, ?Journal of Economic Inequality?, Vol. 10, http://dx.doi.org/10.1007/s10888-011-9188-x.
Flowerdew R. (2011), How serious is the Modifiable Areal Unit Problem for analysis of English census data?, ?Population Trends?, No 145, http://dx.doi.org/10.1057/pt.2011.20.
Goraj L., Cholewa I., Osuch D., Płonka R. (2010), Analiza skutków zmian we Wspólnotowej Typologii Gospodarstw Rolnych, Instytut Instytut Ekonomiki Rolnictwa i Gospodarki Żywnościowej - Państwowy Instytut Badawczy, Warszawa.
Holt D., Steel D.G., Tranmer M. (1996), Area homogeneity and the modifiable areal unit problem, ?Geographical Systems?, Vol. 3.
Fotheringharn, A.S., Wong D.W.S. (1991), The modifiable area unit problem in multivariate analysis, ?Environment und Planning A?, Vol. 23.
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?, Vol. 29, http://dx.doi.org/10.2307/2277827.
Manley D., Flowerdew R., Steel D. (2006), Scales, levels and processes: Studying spatial patterns of British census variables Computers, ?Environment and Urban Systems?, Vol. 30.
Marble D.F. (2000), Some thoughts on the integration of spatial analysis and Geographic Information Systems, ?Journal of Geographical Systems?, Vol. 2, http://dx.doi.org/10.1007/s101090050026.
Michna W. (2005), Zróżnicowanie funkcji gospodarstw rolnych w ujęciu przestrzennym, Instytut Ekonomiki Rolnictwa i Gospodarki Żywnościowej ? Państwowy Instytut Badawczy, Warszawa.
Openshaw S. (1977a), A geographical solution to scale and aggregation problems in region-building, partitioning and spatial modelling, ?Transactions of the Institute of British Geographers?, New Series, Vol. 2, http://dx.doi.org/10.2307/622300.
Openshaw S. (1977b), Algorithm 3: a procedure to generate pseudo-random aggregationsof N zones into M zones, where M is less than N', ?Environment and Planning A?, Vol. 9.
Openshaw S. (1977c), Optimal zoning systems for spatial interaction models, ?Environment and Planning A?, Vol. 9, http://dx.doi.org/10.1068/a090169.
Openshaw S., Taylor P.J. (1979), A million or so correlation coefficients: three experiments on the modifiable areal unit problem, [in:] Wrigley N. (ed.), Statistical methods in the spatial sciences, London: Pion.
Openshaw S. (1984a), The Modifiable Areal Unit Problem, GeoBooks, CATMOG 38, Norwich.
Openshaw S. (1984b), Ecological fallacies and the analysis of areal census data, ?Environment and Planning A?, Vol. 16, http://dx.doi.org/10.1068/a160017.
Paelinck J.H.P. (2000), On aggregation in spatial econometric modelling, ?Journal of Geographical Systems?,Vol. 2, http://dx.doi.org/10.1007/PL00011452 .
Pietrzak M. B. (2010a), Analiza danych przestrzennych a jakość informacji, [in:] Trzaskalik T. (ed.), Modelowanie preferencji a ryzyko '09, Wydawnictwo Uniwersytetu Ekonomicznego, Katowice.
Pietrzak M. B. (2010b), Problem identyfikacji struktury danych przestrzennych, ?Acta Universitatis Nicolai Copernici Ekonomia?, XLI, z. 397, s. 83-98.
Pietrzak M. B. (2013), Interpretation of Structural Parameters for Models with Spatial Autoregression, ?Equilibrium? Vol. 8 I. 2,, s. 129-155, http://dx.doi.org/ 10.12775/EQUIL.2013.010 .
Pietrzak M. B., (2014a), Redefining the modifiable areal unit problem within spatial econometrics, the case of the scale problem, ?Equilibrium? Volume 9, Issue 2 (forthcoming).
Pietrzak M. B. (2014b), The modifiable areal unit problem - analysis of correlation and regression, ?Equilibrium?, Volume 9, Issue 4 (forthcoming).
Pietrzak M.B, Wilk J,. Kossowski T., Bivand R. (2014), The identification of spatial dependence in the analysis of regional economic development - join-count test application, [in:] Papież M. & Śmiech S. (ed.), Proceedings of 8th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, Cracow: Foundation of the Cracow University of Economics (forthcoming).
Reynolds H. D. (1998), The Modifiable Area Unit Problem: Empirical Analysis by Statistical Simulation, doctoral thesis, graduate Deparment of Geography, University of Toronto.
Roberts K.D. (1982), Agrarian structure and labor mobility in rural Mexico, ?Population and Development Review?, Vol. 8, http://dx.doi.org/10.2307/1972988.
Robinson W.S. (1950), Ecological Correlations and the Behavior of Individuals, ?American Sociological Review?, Vol. 15, No. 3, http://dx.doi.org/10.2307/2087176.
Skarżyńska A., Goraj L., Ziętek I. (2005), Metodologia SGM ?2002? dla typologii gospodarstw rolnych w Polsce, Instytut Instytut Ekonomiki Rolnictwa i Gospodarki Żywnościowej - Państwowy Instytut Badawczy, Warszawa.
Suchecki B. (ed.) (2010), Ekonometria Przestrzenna. Metody i modele analizy danych przestrzennych, Wydawnictwo C.H.Beck, Warszawa.
Szulc E. (2007), Ekonometryczna analiza wielowymiarowych procesów gospodarczych, Wydawnictwo UMK, Toruń.
Tate N., Atkinson P.M. (ed.) (2001), Modelling scale in geographical information science, John Wiley & Sons, Chichester.
Tranmer M., Steel D. (2001), Using Local Census Data to Investigate Scale Effects [in:] Tate N., Atkinson P. (ed.), Modelling scale in geographical information science, Chichester: John Wiley & Sons.
Woś A. (ed.) (1998), Encyklopedia agrobiznesu, Fundacja Innowacja, Warszawa.
Yule G.U., Kendall M.G. (1950), An introduction to the theory of statistics, Griffin, London.
Downloads
Published
2014-09-30
How to Cite
Pietrzak, M. B. (2014). Redefining the Modifiable Areal Unit Problem Within Spatial Econometrics, the Case of the Aggregation Problem. Equilibrium. Quarterly Journal of Economics and Economic Policy, 9(3), 131–151. https://doi.org/10.12775/EQUIL.2014.021
Issue
Section
Varia
