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Semiparametric filtering of spatial autocorrelation: the eigenvector approach

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  • Michael Tiefelsdorf
  • Daniel A Griffith

Abstract

In the context of spatial regression analysis, several methods can be used to control for the statistical effects of spatial dependencies among observations. Maximum likelihood or Bayesian approaches account for spatial dependencies in a parametric framework, whereas recent spatial filtering approaches focus on nonparametrically removing spatial autocorrelation. In this paper we propose a semiparametric spatial filtering approach that allows researchers to deal explicitly with (a) spatially lagged autoregressive models and (b) simultaneous autoregressive spatial models. As in one nonparametric spatial filtering approach, a specific subset of eigenvectors from a transformed spatial link matrix is used to capture dependencies among the disturbances of a spatial regression model. However, the optimal subset in the proposed filtering model is identified more intuitively by an objective function that minimizes spatial autocorrelation rather than maximizes a model fit. The proposed objective function has the advantage that it leads to a robust and smaller subset of selected eigenvectors. An application of the proposed eigenvector spatial filtering approach, which uses a cancer mortality dataset for the 508 US State Economic Areas, demonstrates its feasibility, flexibility, and simplicity.

Suggested Citation

  • Michael Tiefelsdorf & Daniel A Griffith, 2007. "Semiparametric filtering of spatial autocorrelation: the eigenvector approach," Environment and Planning A, Pion Ltd, London, vol. 39(5), pages 1193-1221, May.
  • Handle: RePEc:pio:envira:v:39:y:2007:i:5:p:1193-1221
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    Cited by:

    1. Christoph Grimpe & Roberto Patuelli, 2011. "Regional knowledge production in nanomaterials: a spatial filtering approach," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 46(3), pages 519-541, June.
    2. José Villaverde & Adolfo Maza, 2012. "Chinese per Capita Income Distribution, 1992–2007: A Regional Perspective," Asian Economic Journal, East Asian Economic Association, vol. 26(4), pages 313-331, December.
    3. Yongwan Chun, 2008. "Modeling network autocorrelation within migration flows by eigenvector spatial filtering," Journal of Geographical Systems, Springer, vol. 10(4), pages 317-344, December.
    4. Clément Gorin, 2016. "Patterns and determinants of inventors’ mobility across European urban areas," Working Papers 1615, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    5. repec:bla:presci:v:96:y:2017:i:2:p:357-380 is not listed on IDEAS
    6. Christoph Hammer & Aurélien Fichet de Clairfontaine, 2016. "Trade Costs and Income in European Regions," Department of Economics Working Papers wuwp220, Vienna University of Economics and Business, Department of Economics.
    7. Yongwan Chun & Daniel A. Griffith & Monghyeon Lee & Parmanand Sinha, 2016. "Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters," Journal of Geographical Systems, Springer, vol. 18(1), pages 67-85, January.
    8. Crespo Cuaresma, Jesus & Doppelhofer, Gernot & Huber, Florian & Piribauer, Philipp, 2015. "Growing Together? Projecting Income Growth in Europe at the Regional Level," Department of Economics Working Paper Series 4583, WU Vienna University of Economics and Business.
    9. repec:eee:ecomod:v:207:y:2007:i:2:p:234-242 is not listed on IDEAS
    10. Csereklyei, Zsuzsanna & Stern, David I., 2015. "Global energy use: Decoupling or convergence?," Energy Economics, Elsevier, vol. 51(C), pages 633-641.
    11. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    12. Sandy Burden & Noel Cressie & David G. Steel, 2015. "The SAR Model for Very Large Datasets: A Reduced Rank Approach," Econometrics, MDPI, Open Access Journal, vol. 3(2), pages 1-22, May.
    13. Aurélien Fichet de Clairfontaine & Manfred Fischer & Rafael Lata & Manfred Paier, 2015. "Barriers to cross-region research and development collaborations in Europe: evidence from the fifth European Framework Programme," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 54(2), pages 577-590, March.
    14. An Liu & Henk Folmer & Johan Oud, 2011. "W-based versus latent variables spatial autoregressive models: evidence from Monte Carlo simulations," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 47(3), pages 619-639, December.
    15. Haining, Robert & Law, Jane & Griffith, Daniel, 2009. "Modelling small area counts in the presence of overdispersion and spatial autocorrelation," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2923-2937, June.
    16. Seya, Hajime & Yamagata, Yoshiki & Tsutsumi, Morito, 2013. "Automatic selection of a spatial weight matrix in spatial econometrics: Application to a spatial hedonic approach," Regional Science and Urban Economics, Elsevier, vol. 43(3), pages 429-444.
    17. Jesús Mur & Jean Paelinck, 2011. "Deriving the W-matrix via p-median complete correlation analysis of residuals," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 47(2), pages 253-267, October.
    18. Herrera Gómez, Marcos & Cid, Juan Carlos & Paz, Jorge Augusto, 2012. "Introducción a la econometría espacial: Una aplicación al estudio de la fecundidad en la Argentina usando R
      [Introduction to Spatial Econometrics: An application to the study of fertility in Argent
      ," MPRA Paper 41138, University Library of Munich, Germany.
    19. Jesùs Mur, 2013. "Causality, Uncertainty and Identification: Three Issues on the Spatial Econometrics Agenda," SCIENZE REGIONALI, FrancoAngeli Editore, vol. 2013(1), pages 5-27.
    20. Daisuke Murakami & Daniel Griffith, 2015. "Random effects specifications in eigenvector spatial filtering: a simulation study," Journal of Geographical Systems, Springer, vol. 17(4), pages 311-331, October.
    21. Florian Schoiswohl & Philipp Piribauer & Michael Gmeinder & Matthias Koch & Manfred Fischer, 2012. "The Speed of Income Convergence in Europe: A case for Bayesian Model Averaging with Eigenvector Filtering," ERSA conference papers ersa12p744, European Regional Science Association.
    22. Manfred M. Fischer & Daniel A. Griffith, 2008. "Modeling Spatial Autocorrelation In Spatial Interaction Data: An Application To Patent Citation Data In The European Union," Journal of Regional Science, Wiley Blackwell, vol. 48(5), pages 969-989.
    23. Clément Gorin, 2016. "Patterns and determinants of inventors' mobility across European urban areas," Working Papers halshs-01313086, HAL.

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