Constructing the Spatial Weights Matrix Using a Local Statistic

  • Arthur GetisEmail author
  • Jared Aldstadt
Part of the Advances in Spatial Science book series (ADVSPATIAL)


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.


Spatial Autocorrelation Spatial Association Variogram Model Autocorrelation Coefficient Spatial Weight Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors greatly appreciate the comments of Michael Tiefelsdorf and three anonymous reviewers. The paper has been considerably strengthened due to their suggestions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of GeographySan Diego State UniversitySan DiegoUSA
  2. 2.Department of GeographyUniversity at BuffaloBuffaloUSA

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