Full-text resources of CEJSH and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


2020 | 50 | 159-174

Article title

Wybrane zagadnienia modelowania matematyczno-statystycznego struktur i procesów przestrzennych

Content

Title variants

EN
Mathematical and statistical modeling of spatial structures and processes: selected issues

Languages of publication

PL

Abstracts

PL
Niniejsze opracowanie jest przeglądem wybranych zagadnień z zakresu modelowania matematyczno-statystycznego struktur i procesów przestrzennych. Ogólny charakter tego artykułu obejmuje dyskusję nad podstawowymi pojęciami, takimi jak: układ przestrzenny, struktura przestrzenna, proces przestrzenny, i ich wzajemnymi relacjami. Następnie definiowany jest w sposób ogólny (stochastyczny) proces przestrzenny i jego składniki, ze szczególnym uwzględnieniem reprezentacji struktury przestrzennej. Artykuł omawia sposób budowy modelu stochastycznego procesu przestrzennego, analizując jednocześnie najważniejsze problemy pojawiające się na etapie jego specyfikacji, estymacji i weryfikacji. Uwypuklono również wkład poznańskich geografów w rozwiązywanie problemów teoretycznych związanych z modelowaniem struktur i procesów przestrzennych.
EN
This study is a review of selected issues in mathematical and statistical modeling of spatial structures and processes. The review includes a discussion of basic concepts such as spatial pattern, spatial structure and spatial process and their relationships. Then, a general (stochastic) spatial process and its components are defined with a special focus on the problem of the spatial structure representation. The article discusses a procedure of constructing a stochastic spatial process model, and analyses the most important problems that arise during the specification, estimation and validation of the model. The Polish contribution to solving theoretical questions related to the modeling of spatial structures and processes was also emphasized.

Year

Issue

50

Pages

159-174

Physical description

Dates

published
2020-10-15

Contributors

  • Wydział Geografii Społeczno-Ekonomicznej i Gospodarki Przestrzennej, Uniwersytet im. Adama Mickiewicza w Poznaniu

References

  • Anselin L. 1988. Spatial Econometrics: Methods and Models. Kluwer, Dordrecht.
  • Barry R., Pace R. 1999. Monte Carlo Estimates of the Log Determinant of Large Sparse Matrices. Linear Algebra and Its Applications, 289: 41–54.
  • Anselin L. 1995. Local Indicators of Spatial Association-LISA. Geographical Analysis, 27: 93–115.
  • Anselin L., Florax R.J.G.M (red.) 1995. New Directions in Spatial Econometrics. Springer-Verlag, Berlin.
  • Anselin, L., Li, X. 2019. Operational local join count statistics for cluster detection. J. Geogr. Syst., 21: 189–210.
  • Bhattacharjee A., Jensen-Butler C. 2013. Estimation of the spatial weights matrix under structural constrains. Regional Science and Urban Economics, 43: 617–634.
  • 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., Hauke J., Kossowski T. 2013. Computing the Jacobian in Spatial Autoregressive Models: An Illustrated Comparison of Available Methods. Geographical Analysis, 45, 2: 150–179
  • Bivand R.S., Wilk J., Kossowski T. 2017. Spatial association of population pyramids across Europe: The application of symbolic data, cluster analysis and join-count tests. Spatial Statistics, 21: 339–361.
  • 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.
  • Florax R.J., Rey S. 1995. The impact of misspecified spatial interaction in linear regression models. [W:] L. Anselin, R.J. Florax (red.), New Directions in Spatial Econometrics, s. 111–135.
  • Florax R.J.G.M., Folmer H., Rey S.J. 2003. Specification searches in spatial econometrics: the relevance of Hendry’s methodology. Regional Science and Urban Economics, 33: 557–579.
  • Florax R.J.G.M., Folmer H., Rey S.J. 2005. A comment on specification searches in spatial econometrics: the relevance of Hendry’s methodology: A reply. Regional Science and Urban Economics, 36: 557–579.
  • Folmer H., Oud J.H. 2008. How to get more rid of W: a latent variables approach to modelling spatially lagged variables. Environment and Planning, A 40: 2526–2538.
  • Fotheringham A.S. 2009. The Problem of Spatial Auctocorrelation and Local Spatial Statistics. Geographical Analysis, 41: 398–403.
  • Fotheringham A.S., Brundson C., Charlton M. 2002. Geographically Weighted Regression. Wiley & Sons, Chichester.
  • Geary R. 1954. The Contiguity Ratio and Statistical Mapping. The Incorporated Statistician, 5: 115–145.
  • Getis A., Aldstadt J. 2004. Constructing the Spatial Weights Matrix Using a Local Statistic. Geographical Analysis, 36: 90–104.
  • Griffith D.A., Sone A. 1995. “Trade-offs Associated with Normalizing Constant Computational Simplifications for Estimating Spatial Statistical Models. Journal of Statistical Computation and Simulation, 51: 165–83.
  • Haining R.P. 1978. Estimating Spatial Interaction Models. Environment and Planning, A, 10: 305–320.
  • Haining R. 1990. Spatial Data Analysis in the Social and Environmental Sciences. Cambridge University Press, Cambridge.
  • Hays J.C., Kachi A., Franzese R.J. 2010. A spatial model incorporating dynamic, endogenous network interdependence: A political science application. Statistical Methodology, 7: 406–428.
  • Herrera M., Mur J., Ruiz M. 2018. A Comparison Study on Criteria to Select the Most Adequate Weighting Matrix. Entropy, 21, 2: 160.
  • Kelejian H.H., Prucha I. 2002. 2SLS and OLS in spatial autoregressive model with equal weights. Regional Science and Urban Economics, 32: 691–707.
  • Kelejian H.H., Prucha I. 1998. A Generalized 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. A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review, 40, 2: 509–533.
  • Kelejian H.H., Prucha I. 2010. Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. Journal of Econometrics, 157: 53–67.
  • Kelejian H.H., Piras G. 2014. Estimation of spatial models with endogenous weighting matrices, and an application to a demand model for cigarettes. Regional Science and Urban Economics, 46: 140–149.
  • Kooijman S. 1976. Some remarks on the statistical analysis of grids especially with respect to ecology. Annals of System Research, 5: 113–132.
  • 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., 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.
  • Kossowski T.M., Hauke J. 2011. The method of computing the Log-Jacobian of the variable transformation for spatial models-test and comments. Acta Universitatis Lodziensis, Folia Oeconomica, 252: 161–173.
  • Lee L.-F. 2007. GMM and 2SLS estimation of mixed regressive, spatial autoregressive models. Journal of Econometrics, 137: 489–514.
  • Lee L.F., Yu J. 2012. QML estimation of spatial dynamic panel data models with time-varying spatial weights matrices. Spatial Economic Analysis, 7: 31–74.
  • LeSage J.P., Pace R.K. 2014. The biggest myth in spatial econometrics. Econometrics, 2, 217–249.
  • Moran P.A.P. 1950. Notes on continuous stochastic phenomena. Biometrika, 37: 17–23.
  • Mur J., Hauke J., Kossowski T. 2019. Searching for the spatial weighting matrix. A GMM approach to W. Manuscript submitted to Sankhya A.
  • Ord J. 1975. Estimation Methods for Models of Spatial Interaction. Journal of the American Statistical Association, 70: 120–26.
  • Qu X., Lee L.F. 2015. Estimating a spatial autoregressive model with an endogenous spatial weighting matrix. Journal of Econometrics: 209–232.
  • Pace R., Barry R. 1997. Sparse Spatial Autoregressions. Statistics and Probability Letters, 33: 291–97.
  • Pace R., LeSage J. 2004. Chebyshev Approximation of Log-Determinants of Spatial Weight Matrices. Computational Statistics and Data Analysis 45: 179–96.
  • Ratajczak W. 1980. Analiza i modele wpływu czynników społeczno-gospodarczych na kształtowanie się sieci transportowych. PAN, seria Geografia, 5. PWN, Warszawa.
  • 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.
  • Ripley B. 1981. Spatial Statistics. Wiley, New York.
  • Smirnov O., Anselin L. 2001. Fast Maximum Likelihood Estimation of Very Large Spatial Autoregressive Models: A Characteristic Polynomial Approach. Computational Statistics and Data Analysis, 35: 301–319.
  • Smirnov O., Anselin L. 2009. An O(N) Parallel Method of Computing the Log-Jacobian of the Variable Transformation for Models with Spatial Interaction on A Lattice. Computational Statistics and Data Analysis, 53: 2980–2988.
  • Tiefelsdorf M. 2000. Modeling spatial processes: the identification and analysis of spatial relationships in regression residuals by means of Moran’s I. Springer, Berlin–Heidelberg.
  • 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.
  • Whittle P. 1954. On Stationary Process in the Plane. Biometrika, 41: 434–449.
  • Whittle P. 1963. Stochastic Processes in Several Dimensions. Bulletin of the International Statistical Institute, 40: 974–994.

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.ojs-doi-10_14746_rrpr_2020_50_09
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.