Gaussian Markov Random Fields versus Linear Mixed Models for satellite-based PM_2.5 assessment: Evidence from the Northeastern USA

Studying the effects of air-pollution on health is a key area in environmental epidemiology. An accurate estimation of air-pollution effects requires spatio-temporally resolved datasets of air-pollution, especially, Fine Particulate Matter (PM). Satellite-based technology has greatly enhanced the ability to provide PM assessments in locations where direct measurement is impossible. Indirect PM measurement is a statistical prediction problem. The spatio-temporal statistical literature offer various predictive models: Gaussian Random Fields (GRF) and Linear Mixed Models (LMM), in particular. GRF emphasize the spatio-temporal structure in the data, but are computationally demanding to fit. LMMs are computationally easier to fit, but require some tampering to deal with space and time. Recent advances in the spatio-temporal statistical literature propose to alleviate the computation burden of GRFs by approximating them with Gaussian Markov Random Fields (GMRFs). Since LMMs and GMRFs are both computationally feasible, the question arises: which is statistically better? We show that despite the great popularity of LMMs in environmental monitoring and pollution assessment, LMMs are statistically inferior to GMRF for measuring PM in the Northeastern USA.