Regionalization of Multiscale Spatial Processes using a Criterion for Spatial Aggregation Error

TL;DR

This paper introduces a new criterion called CAGE for optimizing regionalization of spatial data to minimize aggregation errors, linking it to multiscale K-L expansion and demonstrating its effectiveness on real datasets.

Contribution

It proposes a novel criterion for spatial aggregation error (CAGE) and connects it to multiscale K-L expansion, advancing methods for optimal regionalization in spatial analysis.

Findings

CAGE effectively guides regionalization to reduce aggregation error.

Theoretical links between CAGE, prediction error, and spatial variance are established.

Application to real datasets shows improved spatial support selection.

Abstract

The modifiable areal unit problem and the ecological fallacy are known problems that occur when modeling multiscale spatial processes. We investigate how these forms of spatial aggregation error can guide a regionalization over a spatial domain of interest. By "regionalization" we mean a specification of geographies that define the spatial support for areal data. This topic has been studied vigorously by geographers, but has been given less attention by spatial statisticians. Thus, we propose a criterion for spatial aggregation error (CAGE), which we minimize to obtain an optimal regionalization. To define CAGE we draw a connection between spatial aggregation error and a new multiscale representation of the Karhunen-Loeve (K-L) expansion. This relationship between CAGE and the multiscale K-L expansion leads to illuminating theoretical developments including: connections between spatial aggregation error, squared prediction error, spatial variance, and a novel extension of Obled-Creutin eigenfunctions. The effectiveness of our approach is demonstrated through an analysis of two datasets, one using the American Community Survey and one related to environmental ocean winds.