Global and local spatial autocorrelation in bounded regular tessellations |
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| Authors: | Barry Boots Michael Tiefelsdorf |
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| Institution: | (1) Department of Geography and Environmental Studies, Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5 (bboots@wlu.ca), CA;(2) Department of Geography, The Ohio State University, Columbus, OH 43210, USA (tiefelsdorf.1@osu.edu), US |
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| 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.
Received: 2 July 1999 / Accepted: 9 November 1999 |
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| Keywords: | : Regular planar tessellations global and local spatial autocorrelation spatial correlogram increasing-domain asymptotics spatial eigenfunctions |
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