Abstract
Spatial modeling is currently one of the primary research tools used in regional analysis. Spatial models are an extension of traditional econometric models, which are included in the so called spatial effects: spatial dependence and spatial heterogeneity. The article presents the theoretical basis of spatial modelling, together with definitions of basic concepts and an analysis of their properties. Methods for estimating spatial models and diagnostics are presented. The study also indicates the complexity of spatial modeling, and the usefulness of this kind research approach. In this paper an outline the development trends of spatial modeling is delivered.
References
Anselin L. 1988. Spatial Econometrics: Methods and Models. Kluwer, Dordrecht.
Anselin L. 1988a. Lagrange Multiplier Test Diagnostics for Spatial Dependence and Spatial Heterogeneity. Geographical Analysis, 20: 1–17.
Anselin L. 1994. Testing for Spatial Dependence in Linear Regression Models: A Review. West Virginia University, Morgantown, Regional Research Institute Research Paper, s. 94–116.
Anselin L., Florax R.J.G.M. (red.) 1995. New Directions in Spatial Econometrics. Springer- Verlag, Berlin.
Anselin L., Bera A.K., Florax R.J.G.M., Yoon M.J. 1996. Simple diagnostic tests for spatial dependence. Regional Science and Urban Economics, 26: 77–104.
Anselin L., Moreno R. 2003. Properties of tests for spatial error components. Regional Science and Urban Economics, 33: 595–618.
Bera A., Yoon M. 1992. Simple Diagnostic Tests for Spatial Dependence. University of Illinois, Urbana-Champaign.
Bivand R.S. 1984. Regression Modelling with Spatial Dependence: An Application of Some Class Selection and Estimation Methods. Geographical Analysis, 16: 25–37.
Bivand R. 2008. Power calculations for global and local Moran’s I. Computational Statistics and Data Analysis, 53, 8: 2859–2872.
Boots B., Tiefelsdorf M. 2000. Global and local spatial autocorrelation in bounded regular tessalations. Journal of Geographical Systems, 2: 319–348.
Burridge P. 1980. On the Cliff-Ord Test for Spatial Autocorrelation. Journal of The Royal Statistical Society B, 42: 107–108.
Cliff A.D., Ord J.K. 1970. Spatial Autocorrelation: A Review of Existing and New Measures with Applications. Economic Geography, 46: 269–272.
Cliff A.D., Ord J.K. 1972. Testing for Spatial Autocorrelation Among Regression Residuals. Geographical Analysis, 4: 267–284.
Cliff A.D., Ord J.K. 1973. Spatial Autocorrelation. Pion, London.
Cliff A.D., Ord J.K. 1981. Spatial Processes: Models and Applications. Pion, London.
Geary R. 1954. The Contiguity Ratio and Statistical Mapping. The Incorporated Statistician, 5: 115–145.
Getis A. 2007. Reflections on spatial autocorrelation. Regional Science and Urban Economics, 37: 491–496.
Getis A., Aldstadt J. 2004. Constructing the Spatial Weights Matrix Using a Local Statistic. Geographical Analysis, 36: 90–104.
Getis A., Ord J.K. 1992. The Analysis of Spatial Association by Use of Distance Statsitsics. Geographical Analysis, 24: 189–206.
Griffith D.A. 1996. Some Guidelines for Specifying the Geographic Weights Matrix Contained in Spatial Statistical Models. [W:] S.L. Arlinghaus (red.), Practical Handbook of Spatial Statistics. CRC, Boca Raton.
Griffith D.A. 2000. Eigenfunction properties and approximation of selected incidence matrices employed in spatial analysis. Linear Algebra and its Applications, 321: 95–112.
Griffith D.A. 2003. Spatial Autocorrelation and Spatial Filtering, Springer, Berlin–Heidelberg.
Griffith D.A. 2004. Extreme eigenfunctions of adjacency matrices for planar graphs employed in spatial analyses. Linear Algebra and its Applications, 388: 201–219.
Griffith D.A. 2010. The Moran coefficient for non-normal data. Journal of Statistical Planning and Inference, 140: 2980–2990.
Haining R.P. 1978. Estimating Spatial Interaction Models. Environment and Planning A, 10: 305–320.
Haining R.P. 1995. Data problems in spatial econometric modeling. [W:] L. Anselin, R.J.G.M. Florax (red.), New Directions in Spatial Econometrics. Springer-Verlag, Berlin, s. 156–171.
Hauke J., Kossowski T. 2008. Moran’s coefficient and algebraic characteristics of some standardized connectivity matrices used to measure a spatial autocorrelation. Working Paper of The 17th International Workshop in Matrices and Statistics in honour of Professor Theodore Wilbur Anderson 90th birthday, July 23–26. Tomar, Portugal.
Janc K. 2006. Zjawisko autokorelacji przestrzennej na przykładzie statystyki I Morana oraz lokalnych wskaźników zależności przestrzennej (LISA) – wybrane zagadnienia metodyczne. [W:] T. Komornicki, Z. Podgórski (red.), Idee i praktyczny uniwersalizm geografii. Dokumentacja Geograficzna, 33: 76–83.
Janc K. 2007. Wpływ kapitału ludzkiego na efektywność gospodarek lokalnych w Polsce – przykład zastosowania regresji przestrzennej. [W:] P. Brezdeń, S. Grykień (red.), Regionalny wymiar integracji europejskiej. T. IX. IGiRR, Uniwersytet Wrocławski, Wrocław, s. 87–98.
Kelejian H.H., Prucha I. 1997. 2SLS and OLS in spatial autoregressive model with equal weights. Regional Science and Urban Economics, 32: 691–707.
Kelejian H.H., Prucha I. 1998. AGeneralized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances. Journal of Real Estate Finance and Economics, 17, 1: 99–121.
Kelejian H.H., Prucha I. 1999. Ageneralized moments estimator for the autoregressive parameter in a spatial model. International Economic Review, 40, 2: 509–533.
Kelejian H.H., Tavlas G.S., Hondroyiannis G. 2006. ASpatial ModellingApproach to Contagion Among Emerging Economies. Open Economies Review, 17: 423–441.
Kopczewska K. 2006. Ekonometria i statystyka przestrzenna z wykorzystaniem programu R CRAN. Cedewu.pl, Warszawa.
Kosfeld R., Eckey H.-F., Dreger C. 2006. Regional Productivity and Income Convergence in the Unified Germany, 1992–2000. Regional Studies, 40, 7: 755–767.
Kossowski T. 2006. Modelowanie struktury sieci transportowej regionu wielkopolskiego. Bogucki Wydawnictwo Naukowe, Poznań.
Kossowski T. 2009. Metody i modele ekonometrii przestrzennej. [W:] Z. Zwoliński (red.), GIS – platforma integracyjna geografii. Bogucki Wydawnictwo Naukowe, Poznań, s. 145–165.
Kossowski T. 2009a. Konwergencja przestrzenna – aspekty teoretyczne. [W:] P. Churski (red.), Praktyczne aspekty badań regionalnych – varia. Vol. II. Biuletyn Instytutu Geografii Społeczno-Ekonomicznej i Gospodarki Przestrzennej UAM, Seria Rozwój Regionalny i Polityka Regionalna 8: 7–20.
Kossowski T., Motek P. 2009. Spatial modelling of the local public finance in Poland. [W:] T. Markowski, M. Turała (red.), Theoretical and practical aspects of urban and regional development. Studia Regionalia 24: 152–167.
Lee L.-F. 2007. GMM and 2SLS estimation of mixed regressive, spatial autoregressive models. Journal of Econometrics, 137: 489–514.
Lee S.-I. 2001. Developing a bivariate spatial association measure: An integration of Pearson’s r and Moran’s I. Journal of Geographical Systems, 3: 369–385.
Maddala G.S. 2006. Ekonometria, Wydawnictwo Naukowe PWN, Warszawa.
Maćkiewicz B. 2007. Rynek nieruchomości niezabudowanych w Poznaniu i powiecie poznańskim w latach 1995–2000. Bogucki Wydawnictwo Naukowe, Poznań.
Mobley L., Root E., Anselin L., Lozano N.. Koshinsky J. 2006. Spatial analysis of elderly access to primary care services. International Journal of Health Geographics, 5: 19.
Moran P.A.P. 1950. Notes on continuous stochastic phenomena. Biometrika, 37: 17–23.
Olejnik A. 2008. Using the spatial autoregressively distributed lag model in assessing the regional convergence of per-capita income in the EU25. Papers in Regional Science, 87, 3: 371–384.
Oud J.H.L., Folmer H., Patuelli R., Nijkamp P. 2010. ASpatial-Dependence Continuous- Time Model for Regional Uemployment in Germany. 50th ERSACongress in Jonkoping, Working Paper.
Paelinck J.H.P. 2000. On aggregation in spatial econometric modeling. Journal of Geographical Systems, 2: 157–165.
Paelinck J.H.P., Klaassen L.H. 1979. Spatial Econometrics. Gower, Westmead, Farnborough.
Ratajczak W. 1980. Analiza i modele wpływu czynników społeczno-gospodarczych na kształtowanie się sieci transportowych. PWN, Warszawa–Poznań.
Ratajczak W. 2008. Modele ekonometrii przestrzennej w analizie regionalnej. [W:] T. Stryjakiewicz, T. Czyż (red.), O nowy kształt badań w geografii i gospodarce przestrzennej, Biuletyn KPZK PAN, 237: 186–202.
Suchecki B. (red.) 2010. Ekonometria przestrzenna. Metody i modele analizy danych przestrzennych. Wydawnictwo C.H. Beck, Warszawa.
Tiefelsdorf M., Boots B. 1995. The exact distribution of Moran’s I. Environment and Planning A, 27: 985–999.
Tiefelsdorf M., Griffith D.A., Boots B. 1998. A Variance Stabilizing Coding Scheme for Spatial Link Matrices. Environment and Planning A, 31: 165–180.
Tobler W. 1970. Acomputer model simulating urban growth in Detroit region. Economic Geography, 46, 2: 234–240.
Vazquez E.F. 2010. Empirical versus exogenous spatial weighting matrices: an entropy-based intermediate solution. 50th ERSA Congress in Jonkoping, Working Paper.
Walde J., Larch M., Tappeiner G. 2008. Performance contest between MLE and GMM for huge spatial autoregressive models. Journal of Statistical Computation and Simulation, 78, 2: 151–166.
Ying L.G. 2003. Understanding China’s recent growth experience: Aspatial econometric perspective. The Annals of Regional Science, 37, 4: 613–628.
Zelias A. (red.) 1991. Ekonometria przestrzenna. PWE, Warszawa.
License
Copyright (c) 2018 Rozwój Regionalny i Polityka Regionalna
This work is licensed under a Creative Commons Attribution 4.0 International License.