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.
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- 1.
This point was made to us in correspondence by Michael Tiefelsdorf, the editor of this article.
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Acknowledgements
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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Getis, A., Aldstadt, J. (2010). Constructing the Spatial Weights Matrix Using a Local Statistic. In: Anselin, L., Rey, S. (eds) Perspectives on Spatial Data Analysis. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01976-0_11
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DOI: https://doi.org/10.1007/978-3-642-01976-0_11
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