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How to get rid of W: a latent variables approach to modelling spatially lagged variables

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  • Henk Folmer
  • Johan Oud

Abstract

In this paper we propose a structural equation model (SEM) with latent variables to model spatial dependence. Rather than using the spatial weights matrix W, we propose to use latent variables to represent spatial dependence and spillover effects, of which the observed spatially lagged variables are indicators. This approach allows us to incorporate and test more information on spatial dependence and offers more flexibility than the representation in terms of Wy or Wx. Furthermore, we adapt the ML estimator included in the software package Mx to estimate SEMs with spatial dependence. We present illustrations based on Anselin’s Columbus, Ohio, crime dataset.

Suggested Citation

  • Henk Folmer & Johan Oud, 2008. "How to get rid of W: a latent variables approach to modelling spatially lagged variables," Environment and Planning A, Pion Ltd, London, vol. 40(10), pages 2526-2538, October.
  • Handle: RePEc:pio:envira:v:40:y:2008:i:10:p:2526-2538
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    Cited by:

    1. Luisa Corrado & Bernard Fingleton, 2012. "Where Is The Economics In Spatial Econometrics?," Journal of Regional Science, Wiley Blackwell, vol. 52(2), pages 210-239, May.
    2. Jesus Mur & Marcos Herrera & Manuel Ruiz, 2011. "Selecting the W Matrix. Parametric vs Nonparametric Approaches," ERSA conference papers ersa11p1055, European Regional Science Association.
    3. 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.
    4. 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.
    5. Masayoshi Hayashi & Wataru Yamamoto, 2017. "Information sharing, neighborhood demarcation, and yardstick competition: an empirical analysis of intergovernmental expenditure interaction in Japan," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(1), pages 134-163, February.
    6. 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.
    7. Li, Zhengtao & Folmer, Henk & Xue, Jianhong, 2014. "To what extent does air pollution affect happiness? The case of the Jinchuan mining area, China," Ecological Economics, Elsevier, vol. 99(C), pages 88-99.
    8. Michael Brady & Elena Irwin, 2011. "Accounting for Spatial Effects in Economic Models of Land Use: Recent Developments and Challenges Ahead," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 48(3), pages 487-509, March.
    9. Stanislav Stakhovych & Tammo H.A. Bijmolt, 2009. "Specification of spatial models: A simulation study on weights matrices," Papers in Regional Science, Wiley Blackwell, vol. 88(2), pages 389-408, June.
    10. Solmaria Halleck Vega & J. Paul Elhorst, 2014. "Modelling regional labour market dynamics in space and time," Papers in Regional Science, Wiley Blackwell, vol. 93(4), pages 819-841, November.
    11. An Liu & Henk Folmer & Johan Oud, 2011. "Estimating regression coefficients by W-based and latent variables spatial autoregressive models in the presence of spillovers from hotspots: evidence from Monte Carlo simulations," Letters in Spatial and Resource Sciences, Springer, vol. 4(1), pages 71-80, March.
    12. Tang, Jianjun & Folmer, Henk & Xue, Jianhong, 2015. "Technical and allocative efficiency of irrigation water use in the Guanzhong Plain, China," Food Policy, Elsevier, vol. 50(C), pages 43-52.
    13. Bhattacharjee, Arnab & Jensen-Butler, Chris, 2013. "Estimation of the spatial weights matrix under structural constraints," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 617-634.
    14. Herrera Gómez, Marcos & Mur Lacambra, Jesús & Ruiz Marín, Manuel, 2012. "Selecting the Most Adequate Spatial Weighting Matrix:A Study on Criteria," MPRA Paper 73700, University Library of Munich, Germany.
    15. Danny Czamanski & Henk Folmer, 2011. "Introduction: some new methods in regional science," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 47(3), pages 493-497, December.
    16. Jianjun Tang & Henk Folmer, 2016. "Latent vs. Observed Variables: Analysis of Irrigation Water Efficiency Using SEM and SUR," Journal of Agricultural Economics, Wiley Blackwell, vol. 67(1), pages 173-185, February.
    17. Herrera Gómez, Marcos & Mur Lacambra, Jesús & Ruiz Marín, Manuel, 2011. "¿Cuál matriz de pesos espaciales?. Un enfoque sobre selección de modelos
      [Which spatial weighting matrix? An approach for model selection]
      ," MPRA Paper 37585, University Library of Munich, Germany.
    18. Yusep Suparman & Henk Folmer & Johan H.L. Oud, 2016. "The willingness to pay for in-house piped water in urban and rural Indonesia," Papers in Regional Science, Wiley Blackwell, vol. 95(2), pages 407-426, June.
    19. Jesus Mur & Antonio Paez, 2011. "Local weighting or the necessity of flexibility," ERSA conference papers ersa11p942, European Regional Science Association.
    20. An Liu & Inge Noback, 2011. "Determinants of regional female labour market participation in the Netherlands," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 47(3), pages 641-658, December.
    21. 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.

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