The analysis of correlation structures among multivariate spatially aggregated data has become increasingly important and poses substantial challenges. This article concerns the development of partial and semi-partial statistics of spatial associations in the context of multivariate spatial areal data extending Moran's I and Geary's C. The proposed statistical tools describe global or local associations among spatially aggregated measurements for pairs of different components conditional on all remaining components. The new statistics are tested through a simulation study and illustrated using aggregated data on the COVID-19 pandemic recorded at the Community level in Spain.

中文翻译：

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多元区域数据空间关联的部分和半部分统计

多元空间聚合数据之间的相关结构分析变得越来越重要，并带来了巨大的挑战。本文涉及在扩展 Moran's I和 Geary's C的多元空间区域数据的背景下，空间关联的部分和半部分统计的发展。提议的统计工具描述了以所有剩余组件为条件的不同组件对的空间聚合测量值之间的全局或局部关联。新统计数据通过模拟研究进行测试，并使用西班牙社区级别记录的 COVID-19 大流行的汇总数据进行说明。