Adaptive predictive principal components for modeling multivariate air pollution

Air pollution monitoring locations are distributed across the United States; however, prediction of measured pollutant concentrations at new locations is often of interest for various purposes, for example, for pollution–health association studies. For a pollution measure like PM2.5 (fine particulate matter) comprised of multiple chemical components, the predictive principal component analysis (PCA) algorithm derives a low‐dimensional representation of component profiles. Geographic covariates and spatial splines help determine the principal component (PC) loadings of the pollution data to give improved prediction accuracy of the PC scores. While predictive PCA can accommodate pollution data of arbitrary dimension, it is currently limited to a small number of preselected geographic covariates. We propose an adaptive predictive PCA algorithm, which automatically identifies a combination of covariates that is most informative in choosing the PC directions in the pollutant space. We show, by means of simulation and empirical studies, that adaptive predictive PCA improves the accuracy of multicomponent pollutant concentration predictions at unmonitored locations.