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Global and local spatial autocorrelation in bounded regular tessellations

Author

Listed:
  • Barry Boots

    (Department of Geography and Environmental Studies, Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5 (bboots@wlu.ca))

  • Michael Tiefelsdorf

    (Department of Geography, The Ohio State University, Columbus, OH 43210, USA (tiefelsdorf.1@osu.edu))

Abstract

. This paper systematically investigates spatially autocorrelated patterns and the behaviour of their associated test statistic Moran's I in three bounded regular tessellations. These regular tessellations consist of triangles, squares, and hexagons, each of increasing size (n=64; 256; 1024). These tesselations can be downloaded at http://geo-www.sbs.ohio-state.edu/faculty/tiefelsdorf/regspastruc/ in several GIS formats. The selection of squares is particularly motivated by their use in raster based GIS and remote sensing. In contrast, because of topological correspondences, the hexagons serve as excellent proxy tessellations for empirical maps in vector based GIS. For all three tessellations, the distributional characteristics and the feasibility of the normal approximation are examined for global Moran's I, Moran's I (k) associated with higher order spatial lags, and local Moran's I i. A set of eigenvectors can be generated for each tessellation and their spatial patterns can be mapped. These eigenvectors can be used as proxy variables to overcome spatial autocorrelation in regression models. The particularities and similarities in the spatial patterns of these eigenvectors are discussed. The results indicate that [i] the normal approximation for Moran's I is not always feasible; [ii] the three tessellations induce different distributional characteristics of Moran's I, and [iii] different spatial patterns of eigenvectors are associated with the three tessellations.

Suggested Citation

  • Barry Boots & Michael Tiefelsdorf, 2000. "Global and local spatial autocorrelation in bounded regular tessellations," Journal of Geographical Systems, Springer, vol. 2(4), pages 319-348, December.
    • Handle: RePEc:kap:jgeosy:v:2:y:2000:i:4:d:10.1007_pl00011461
    DOI: 10.1007/PL00011461
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    Cited by:

    1. Qiang Wang & Shanlian Yang & Menglei Zheng & Fengxiang Han & Youhua Ma, 2019. "Effects of Vegetable Fields on the Spatial Distribution Patterns of Metal(loid)s in Soils Based on GIS and Moran’s I," IJERPH, MDPI, vol. 16(21), pages 1-20, October.
    2. Giuseppe Espa & Giuseppe Arbia & Diego Giuliani, 2013. "Conditional versus unconditional industrial agglomeration: disentangling spatial dependence and spatial heterogeneity in the analysis of ICT firms’ distribution in Milan," Journal of Geographical Systems, Springer, vol. 15(1), pages 31-50, January.
    3. Fen-Jiao Wang & Chang-Lin Mei & Zhi Zhang & Qiu-Xia Xu, 2022. "Testing for Local Spatial Association Based on Geographically Weighted Interpolation of Geostatistical Data with Application to PM2.5 Concentration Analysis," Sustainability, MDPI, vol. 14(21), pages 1-19, November.
    4. Qing Luo & Daniel A. Griffith & Huayi Wu, 2019. "Spatial autocorrelation for massive spatial data: verification of efficiency and statistical power asymptotics," Journal of Geographical Systems, Springer, vol. 21(2), pages 237-269, June.
    5. Cupido, Kyran & Jevtić, Petar & Paez, Antonio, 2020. "Spatial patterns of mortality in the United States: A spatial filtering approach," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 28-38.
    6. Dusan Paredes & Marcelo Lufin & Patricio Aroca, 2012. "The Estimation of Urban Premium Wage Using Propensity Score Analysis: Some Considerations from the Spatial Perspective," Advances in Spatial Science, in: Esteban Fernández Vázquez & Fernando Rubiera Morollón (ed.), Defining the Spatial Scale in Modern Regional Analysis, edition 127, chapter 0, pages 215-236, Springer.
    7. Julie Le Gallo & Antonio Páez, 2013. "Using Synthetic Variables in Instrumental Variable Estimation of Spatial Series Models," Environment and Planning A, , vol. 45(9), pages 2227-2242, September.
    8. Michael Tiefelsdorf & Daniel A Griffith, 2007. "Semiparametric Filtering of Spatial Autocorrelation: The Eigenvector Approach," Environment and Planning A, , vol. 39(5), pages 1193-1221, May.
    9. Hankach, Pierre & Gastineau, Pascal & Vandanjon, Pierre-Olivier, 2022. "Multi-scale spatial analysis of household car ownership using distance-based Moran's eigenvector maps: Case study in Loire-Atlantique (France)," Journal of Transport Geography, Elsevier, vol. 98(C).
    10. Min Xu & Chang-Lin Mei & Na Yan, 2014. "A note on the null distribution of the local spatial heteroscedasticity (LOSH) statistic," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(3), pages 697-710, May.
    11. Moniruzzaman, Md & Páez, Antonio, 2012. "Accessibility to transit, by transit, and mode share: application of a logistic model with spatial filters," Journal of Transport Geography, Elsevier, vol. 24(C), pages 198-205.
    12. Bernard Fingleton, 2023. "Estimating dynamic spatial panel data models with endogenous regressors using synthetic instruments," Journal of Geographical Systems, Springer, vol. 25(1), pages 121-152, January.
    13. Moraga, J. & Duzgun, H.S. & Cavur, M. & Soydan, H., 2022. "The Geothermal Artificial Intelligence for geothermal exploration," Renewable Energy, Elsevier, vol. 192(C), pages 134-149.

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