Cluster-based bagging of constrained mixed-effects models for high spatiotemporal resolution nitrogen oxides...

Accurate estimation of nitrogen dioxide (NO₂) and nitrogen oxide (NO_x) concentrations at high spatiotemporal resolutions is crucial for improving evaluation of their health effects, particularly with respect to short-term exposures and acute health outcomes. For estimation over large regions like California, high spatial density field campaign measurements can be combined with more sparse routine monitoring network measurements to capture spatiotemporal variability of NO₂ and NO_x concentrations. However, monitors in spatially dense field sampling are often highly clustered and their uneven distribution creates a challenge for such combined use. Furthermore, heterogeneities due to seasonal patterns of meteorology and source mixtures between sub-regions (e.g. southern vs. northern California) need to be addressed.

In this study, we aim to develop highly accurate and adaptive machine learning models to predict high-resolution NO₂ and NO_x concentrations over large geographic regions using measurements from different sources that contain samples with heterogeneous spatiotemporal distributions and clustering patterns.

We used a comprehensive Kruskal-K-means method to cluster the measurement samples from multiple heterogeneous sources. Spatiotemporal cluster-based bootstrap aggregating (bagging) of the base mixed-effects models was then applied, leveraging the clusters to obtain balanced and less correlated training samples for less bias and improvement in generalization. Further, we used the machine learning technique of grid search to find the optimal interaction of temporal basis functions and the scale of spatial effects, which, together with spatiotemporal covariates, adequately captured spatiotemporal variability in NO₂ and NO_x at the state and local levels.

We found an optimal combination of four temporal basis functions and 200 m scale spatial effects for the base mixed-effects models. With the cluster-based bagging of the base models, we obtained robust predictions with an ensemble cross validation R² of 0.88 for both NO₂ and NO_x [RMSE (RMSEIQR): 3.62 ppb (0.28) and 9.63 ppb (0.37) respectively]. In independent tests of random sampling, our models achieved similarly strong performance (R² of 0.87-0.90; RMSE of 3.97-9.69 ppb; RMSEIQR of 0.21-0.27), illustrating minimal over-fitting.

Our approach has important implications for fusing data from highly clustered and heterogeneous measurement samples from multiple data sources to produce highly accurate concentration estimates of air pollutants such as NO₂ and NO_x at high resolution over a large region.