Abstract
Because eigenvector spatial filtering (ESF) provides a relatively simple and successful method to account for spatial autocorrelation in regression, increasingly it has been adopted in various fields. Although ESF can be easily implemented with a stepwise procedure, such as traditional stepwise regression, its computational efficiency can be further improved. Two major computational components in ESF are extracting eigenvectors and identifying a subset of these eigenvectors. This paper focuses on how a subset of eigenvectors can be efficiently and effectively identified. A simulation experiment summarized in this paper shows that, with a well-prepared candidate eigenvector set, ESF can effectively account for spatial autocorrelation and achieve computational efficiency. This paper further proposes a nonlinear equation for constructing an ideal candidate eigenvector set based on the results of the simulation experiment.
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Notes
Some negative spatial autocorrelation may be interleaved in a response variable that shows positive spatial autocorrelation (Griffith 2000). However, it is not a prominent component in empirical datasets, and in the literature spatial autocorrelation in residuals has been successfully accounted for with only positive eigenvectors (e.g., Griffith 2003).
The numbers of all positive eigenvectors for the ten tessellations are reported in Table 2.
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Acknowledgments
We appreciate comments from the editor and two anonymous reviewers. This research was supported by the US National Science Foundation under the Geography and Spatial Sciences and Methodology, Measurement, and Statistics Programs (Grant No. BCS-1229223); any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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Chun, Y., Griffith, D.A., Lee, M. et al. Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters. J Geogr Syst 18, 67–85 (2016). https://doi.org/10.1007/s10109-015-0225-3
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DOI: https://doi.org/10.1007/s10109-015-0225-3