Probabilistic Predictive Principal Component Analysis for Spatially-Misaligned and High-Dimensional Air Pollution Data with Missing Observations

• Activity Number: 636 - Statistical Methods of Air Quality and Exposure
• Type: Contributed
• Date/Time: Thursday, August 2, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Phuong T Vu* and Adam A Szpiro
• Companies: University of Washington and University of Washington
• Keywords: air pollution; environmental epidemiology; spatial misalignment; high-dimensional; missing data; dimension reduction

Abstract

Environmental studies often focus on the health impacts of long-term air pollution exposure on human subjects. Pollutant concentrations are measured at regulatory monitoring locations, which are usually located at locations different than the study subjects. This spatial misalignment motivates a two-stage modeling approach with an exposure model and a health regression model. In addition, air pollution is often a mixture of many components with different health implications. Conventional approaches incorporate techniques such as principal component analysis (PCA) to obtain a lower-dimensional representation of the data. Recently developed predictive PCA modifies the optimization criterion to improve the exposure model. However, these approaches require complete data. Real-world data tend to have complex missing patterns, including some pollutants that are measured at relatively few locations and some locations with many missing measures. We propose a probabilistic predictive PCA (ProPrPCA) that allows for flexible imputation to utilize all available monitoring data. We demonstrate the performance of ProPrPCA with simulations and analysis of multivariate air pollution data.