Spatial Weights Matrix
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Spatial Weights Matrix X IAOBO Z HOU , H ENRY L IN Department of Crop and Soil Sciences, The Pennsylvania State University, University Park, PA, USA Synonyms Spatial weighting matrix; Proximity matrix; Continuity matrix Definition A spatial weights matrix is an n × n positive symmetric matrix W with element wij at location i, j for n locations. The values of wij or the weights for each pair of locations are assigned by some preset rules which define the spatial relations among locations and, therefore, determine the spatial autocorrelation statistics. By convention, wii = 0 for the diagonal elements. Main Text There are many ways to define the weights, including contiguity weights, distance weights, and other weights. The simplest form of weights is binary weight where wij = 1 for neighboring locations i and j, or when the distance between location i and j is less than a fixed distance, or for the fixed number of locations nearest to location i. Otherwise, wij = 0. Another widely used weight is the distance inverse weight in which wij = 1/dij α . In this continuous weighting function, the changing rate of weights over distance dij is determined by the parameter α. Other more complicated spatial weights matrices are also used in calculating spatial autocorrelation statistics. Cross References Autocorrelation, Spatial Geary’s C Moran’s I
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