Simultaneous studies of multiple health conditions over geographic areas can be enhanced by the principal component analysis (PCA). However, the presence of spatial autocorrelation may induce nonlinearity that compromises PCA. This article presents an approach that combines the residual standardization method in PCA with a spatial regression method to account for spatial autocorrelation. It first estimates a multivariate simultaneous autoregressive model for parameter estimates and residuals. It then uses the residuals to formulate a standardized matrix for singular value decomposition. Simulation in various scenarios demonstrates that the proposed approach can effectively remove spatial dependent effects between spatial units to capture pure correlation effects within spatial units. Two case studies examine hospitalization and cancer data in Nebraska. The first demonstrates a way to account for spatial dependency in 39 hospitalization conditions over 156 census tracts. The second applies regression residuals to PCA to evaluate potentially elevated cancer risks near two nuclear power plants. The results show that accounting for spatial dependency and explanatory variables can help reveal information about multiple health outcomes.

中文翻译：

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多因变量空间回归：主成分分析和空间自相关

主成分分析 (PCA) 可以增强对地理区域内多种健康状况的同时研究。然而，空间自相关的存在可能会导致影响 PCA 的非线性。本文提出了一种将 PCA 中的残差标准化方法与空间回归方法相结合来解释空间自相关的方法。它首先估计参数估计和残差的多元同时自回归模型。然后使用残差为奇异值分解制定标准化矩阵。在各种场景中的模拟表明，所提出的方法可以有效地消除空间单元之间的空间相关效应，以捕获空间单元内的纯相关效应。两个案例研究检查了内布拉斯加州的住院和癌症数据。第一个演示了在 156 个人口普查区的 39 种住院条件下解释空间依赖性的方法。第二个将回归残差应用于 PCA 以评估两个核电站附近潜在的癌症风险。结果表明，考虑空间依赖性和解释变量有助于揭示有关多种健康结果的信息。