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Constructing the Spatial Weights Matrix Using a Local Statistic

In: Perspectives on Spatial Data Analysis

Author

Listed:
  • Arthur Getis

    (San Diego State University)

  • Jared Aldstadt

    (University at Buffalo)

Abstract

Spatial weights matrices are necessary elements in most regression models where a representation of spatial structure is needed. We construct a spatial weights matrix, W, based on the principle that spatial structure should be considered in a two-part framework, those units that evoke a distance effect, and those that do not. Our two-variable local statistics model (LSM) is based on the G i * local statistic. The local statistic concept depends on the designation of a critical distance, d c , defined as the distance beyond which no discernible increase in clustering of high or low values exists. In a series of simulation experiments LSM is compared to well-known spatial weights matrix specifications – two different contiguity configurations, three different inverse distance formulations, and three semi-variance models. The simulation experiments are carried out on a random spatial pattern and two types of spatial clustering patterns. The LSM performed best according to the Akaike Information Criterion, a spatial autoregressive coefficient evaluation, and Moran’s I tests on residuals. The flexibility inherent in the LSM allows for its favorable performance when compared to the rigidity of the global models.

Suggested Citation

  • Arthur Getis & Jared Aldstadt, 2010. "Constructing the Spatial Weights Matrix Using a Local Statistic," Advances in Spatial Science, in: Luc Anselin & Sergio J. Rey (ed.), Perspectives on Spatial Data Analysis, chapter 0, pages 147-163, Springer.
  • Handle: RePEc:spr:adspcp:978-3-642-01976-0_11
    DOI: 10.1007/978-3-642-01976-0_11
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    Citations

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    Cited by:

    1. Gonzalez Canche, Manuel Sacramento, 2014. "Localized competition in the non-resident student market," Economics of Education Review, Elsevier, vol. 43(C), pages 21-35.
    2. Ozhegov, Evgeniy & Kosolapov, Nikita & Pozolotina, Iuliia, 2017. "On dependence between housing value and school characteristics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 47, pages 28-48.
    3. Mohamed Amara & AbdelRahmen El Lahga, 2016. "Tunisian constituent assembly elections: how does spatial proximity matter?," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(1), pages 65-88, January.
    4. Cho, Seong-Hoon & Roberts, Roland K. & Kim, Seung Gyu, 2011. "Negative externalities on property values resulting from water impairment: The case of the Pigeon River Watershed," Ecological Economics, Elsevier, vol. 70(12), pages 2390-2399.
    5. Manuel S. González Canché, 2017. "The Heterogeneous Non-resident Student Body: Measuring the Effect of Out-Of-State Students’ Home-State Wealth on Tuition and Fee Price Variations," Research in Higher Education, Springer;Association for Institutional Research, vol. 58(2), pages 141-183, March.
    6. Choi, Hyo Shin & Sohn, So Young & Yeom, Ho Jeong, 2018. "Technological composition of US metropolitan statistical areas with high-impact patents," Technological Forecasting and Social Change, Elsevier, vol. 134(C), pages 72-83.
    7. Wozniak, Marcin, 2021. "Spatial matching on the urban labor market: estimates with unique micro data," Journal for Labour Market Research, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany], vol. 55(55), pages 1-.11.
    8. Wozniak, Marcin, 2021. "Spatial matching on the urban labor market: estimates with unique micro data," Journal for Labour Market Research, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany], vol. 55, pages 1-11.
    9. repec:iab:iabjlr:v:55:i::p:art.11 is not listed on IDEAS
    10. Marcin Wozniak, 2021. "Spatial matching on the urban labor market: estimates with unique micro data," Journal for Labour Market Research, Springer;Institute for Employment Research/ Institut für Arbeitsmarkt- und Berufsforschung (IAB), vol. 55(1), pages 1-17, December.
    11. Greig, Clara & Robertson, Colin & Lacerda, André E.B., 2018. "Spectral-temporal modelling of bamboo-dominated forest succession in the Atlantic Forest of Southern Brazil," Ecological Modelling, Elsevier, vol. 384(C), pages 316-332.
    12. Leopoldo Catania & Anna Gloria Billé, 2017. "Dynamic spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1178-1196, September.
    13. Anna Gloria Billé & Leopoldo Catania, 2018. "Dynamic Spatial Autoregressive Models with Time-varying Spatial Weighting Matrices," BEMPS - Bozen Economics & Management Paper Series BEMPS55, Faculty of Economics and Management at the Free University of Bozen.

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