A novel principal component analysis for spatially misaligned multivariate air pollution data

Abstract

We propose novel methods for predictive (sparse) PCA with spatially misaligned data. These methods identify principal component loading vectors that explain as much variability in the observed data as possible, while also ensuring the corresponding principal component scores can be predicted accurately by means of spatial statistics at locations where air pollution measurements are not available. This will make it possible to identify important mixtures of air pollutants and to quantify their health effects in cohort studies, where currently available methods cannot be used. We demonstrate the utility of predictive (sparse) PCA in simulated data and apply the approach to annual averages of particulate matter speciation data from national Environmental Protection Agency (EPA) regulatory monitors.

Keywords: Air pollution; Dimension reduction; Principal component analysis; Spatial misalignment; Universal kriging.

Fig. 1

Scatterplots of the predictions of the scores without a penalty. These are obtained using cross-validation and UK

Fig. 2

The principal component loadings from two PCA approaches without penalty

Fig. 3

The principal component loadings from two PCA approaches with penalty

Fig. 4

Scatterplots of the predictions of the scores with a penalty to maximize predictability of the pollutants

Fig. 5

Heatmaps based on the predictions of the scores from predictive sparse PCA