Dimension Reduction for Spatially Misaligned Multivariate Air Pollution Data

• Activity Number: 100
• Type: Invited
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: International Indian Statistical Association
• Author(s): Adam Szpiro*+ and Roman Jandarov and Joshua Keller
• Companies: University of Washington and University of Washington and University of Washington
• Keywords: Dimension reduction ; Spatial statistics ; Air pollution ; K-means ; Principal component analysis

Abstract

Emerging monitoring technologies provide high-dimensional characterizations of air pollution. The data are "big" in that they measure multivariate pollution vectors and are comprised of many spatio-temporal observations. Such data promise a more nuanced understanding of which pollutants/mixtures are responsible for health effects previously observed in epidemiology studies, but there are two interrelated challenges (i) interpreting the association parameters requires dimension reduction and (ii) spatial (or spatio-temporal) misalignment between monitor and subject locations requires prediction modeling. We propose a paradigm for spatially predictive dimension reduction, exemplified by predictive sparse principal component analysis and predictive k-means clustering. We seek sparse loading vectors or cluster centers that explain a large proportion of the variance in the monitoring data, while ensuring the corresponding low-dimensional representations are predictable at subject locations. As we demonstrate, this is more effective than dimension reduction followed by spatial prediction, which can result in representations that are difficult to predict at subject locations.