Geographically Weighted Canonical Correlation Analysis: Local Spatial Associations Between Two Sets of Variables

TL;DR

This paper introduces Geographically Weighted Canonical Correlation Analysis (GWCCA), a novel method for analyzing local multivariate spatial associations between two sets of variables, enhancing traditional CCA with spatial localization.

Contribution

The paper proposes GWCCA, extending classical CCA by incorporating spatial weighting to uncover local associations across geographic space.

Findings

GWCCA effectively captures spatial structure in synthetic data.

Application to US health data demonstrates local associations.

GWCCA shows broad potential in spatial data analysis fields.

Abstract

This article critically assesses the utility of the classical statistical technique of Canonical Correlation Analysis (CCA) for studying spatial associations and proposes a new approach to enhance it. Unlike bivariate correlation analysis, which focuses on the relationship between two individual variables, CCA investigates associations between two sets of variables by identifying pairs of linear combinations that are maximally correlated. CCA has strong potential for uncovering complex multivariate relationships that vary across geographic space. We propose Geographically Weighted Canonical Correlation Analysis (GWCCA) as a new technique for exploring local spatial associations between two sets of variables. GWCCA localizes standard CCA by weighting each observation according to its spatial distance from a target location, thereby estimating location-specific canonical correlations. The effectiveness of GWCCA in recovering spatial structure and capturing spatial effects is evaluated using synthetic data. A case study of US county-level health outcomes and social determinants of health further demonstrates the empirical capabilities of the proposed method. The results indicate that GWCCA has broad potential applications in spatial data-intensive fields such as urban planning, environmental science, public health, and transportation, where understanding local multivariate spatial associations is critical.