Implementing Moran eigenvector spatial filtering for massively large georeferenced datasets

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, <i>n</i>, 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.