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.

翻译：本文批判性地评估了经典统计方法典型相关分析（CCA）在研究空间关联中的效用，并提出了一种新的增强方法。与专注于两个单一变量间关系的双变量相关分析不同，CCA通过识别具有最大相关性的线性组合对，来研究两组变量之间的关联。CCA在揭示随地理空间变化的复杂多元关系方面具有巨大潜力。我们提出地理加权典型相关分析（GWCCA）作为一种探索两组变量间局部空间关联的新技术。GWCCA通过根据每个观测点到目标位置的空间距离对其进行加权，从而定位标准CCA，进而估计特定位置的典型相关系数。我们使用合成数据评估了GWCCA在恢复空间结构和捕捉空间效应方面的有效性。一项关于美国县级健康结果与健康社会决定因素的案例研究进一步展示了所提方法的实证能力。结果表明，GWCCA在城市规划、环境科学、公共卫生和交通等空间数据密集型领域具有广泛的应用潜力，这些领域对理解局部多元空间关联至关重要。