Testing spatial heterogeneity in geographically weighted principal components analysis |
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Authors: | Javier Roca-Pardiñas Tomás R Cotos-Yáñez Rubén Pérez-Álvarez |
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Institution: | 1. Department of Statistics, and Operations Research, University of Vigo, Vigo, Spain;2. Department of Transports, and Technology of Projects and Processes, University of Cantabria, Torrelavega, Spain |
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Abstract: | We propose a method to evaluate the existence of spatial variability in the covariance structure in a geographically weighted principal components analysis (GWPCA). The method, that is extensive to locally weighted principal components analysis, is based on performing a statistical hypothesis test using the eigenvectors of the PCA scores covariance matrix. The application of the method to simulated data shows that it has a greater statistical power than the current statistical test that uses the eigenvalues of the raw data covariance matrix. Finally, the method was applied to a real problem whose objective is to find spatial distribution patterns in a set of soil pollutants. The results show the utility of GWPCA versus PCA. |
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Keywords: | Principal components kernel smoothing bandwidth selection soil contamination |
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