Spatial Regression with Multiple Dependent Variables: Principal Component Analysis and Spatial Autocorrelation
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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.
Public Health | Statistics and Probability
Kan, G. L.,
Spatial Regression with Multiple Dependent Variables: Principal Component Analysis and Spatial Autocorrelation.