Constructing the Spatial Weights Matrix Using a Local Statistic

Arthur Getis () and Jared Aldstadt ()
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Arthur Getis: San Diego State University
Jared Aldstadt: University at Buffalo

Chapter Chapter 11 in Perspectives on Spatial Data Analysis, 2010, pp 147-163 from Springer

Abstract: 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.

Keywords: Spatial Autocorrelation; Spatial Association; Variogram Model; Autocorrelation Coefficient; Spatial Weight Matrix (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-01976-0_11

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