Implementing Moran eigenvector spatial filtering for massively large georeferenced datasets

ABSTRACT

Moran eigenvector spatial filtering (MESF) furnishes an alternative method to account for spatial autocorrelation in linear regression specifications describing georeferenced data, although spatial auto-models also are widely used. The utility of this MESF methodology is even more impressive for the non-Gaussian models because its flexible structure enables it to be easily applied to generalized linear models, which include Poisson, binomial, and negative binomial regression. However, the implementation of MESF can be computationally challenging, especially when the number of geographic units, n, is large, or massive, such as with a remotely sensed image. This intensive computation aspect has been a drawback to the use of MESF, particularly for analyzing a remotely sensed image, which can easily contain millions of pixels. Motivated by Curry, this paper proposes an approximation approach to constructing eigenvector spatial filters (ESFs) for a large spatial tessellation. This approximation is based on a divide-and-conquer approach. That is, it constructs ESFs separately for each sub-region, and then combines the resulting ESFs across an entire remotely sensed image. This paper, employing selected specimen remotely sensed images, demonstrates that the proposed technique provides a computationally efficient and successful approach to implement MESF for large or massive spatial tessellations.

KEYWORDS:

• Moran eigenvector spatial filtering
• spatial regression
• spatial autocorrelation
• remotely sensed image

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplementary material

Supplementary data for this article can be accessed here.

Additional information

Notes on contributors

Daniel A. Griffith

Daniel A. Griffith is an Ashbel Smith professor of Geospatial Information Sciences at the University of Texas at Dallas, and works in the areas of spatial statistics, urban economics, and urban public health. Among his many awards is fellow status from the UCGIS and the AAG.

Yongwan Chun

Yongwan Chun is an associate professor of Geospatial Information Sciences at the University of Texas at Dallas. His research interests lie in spatial statistics and GIS focusing on urban issues including population movement, environment, public health, and crime.