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. 2017 Jan;66(1):3-28.
doi: 10.1111/rssc.12148. Epub 2016 Apr 6.

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

Roman A Jandarov  1 , Lianne A Sheppard  2 , Paul D Sampson  2 , Adam A Szpiro  2
Affiliations

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

Roman A Jandarov et al. J R Stat Soc Ser C Appl Stat. 2017 Jan.

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.

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Figures

Fig. 1
Fig. 1
Scatterplots of the predictions of the scores without a penalty. These are obtained using cross-validation and UK
Fig. 2
Fig. 2
The principal component loadings from two PCA approaches without penalty
Fig. 3
Fig. 3
The principal component loadings from two PCA approaches with penalty
Fig. 4
Fig. 4
Scatterplots of the predictions of the scores with a penalty to maximize predictability of the pollutants
Fig. 5
Fig. 5
Heatmaps based on the predictions of the scores from predictive sparse PCA
See this image and copyright information in PMC

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