Global and Geographically and Temporally Weighted Regression Models for Modeling PM 2.5 in Heilongjiang, China from 2015 to 2018

Objective: This study investigated the relationships between PM 2.5 and 5 criteria air pollutants (SO 2 , NO 2 , PM 10 , CO, and O 3 ) in Heilongjiang, China, from 2015 to 2018 using global and geographically and temporally weighted regression models. Methods: Ordinary least squares regression (OLS), linear mixed models (LMM), geographically weighted regression (GWR), temporally weighted regression (TWR), and geographically and temporally weighted regression (GTWR) were applied to model the relationships between PM 2.5 and 5 air pollutants. Results: The LMM and all GWR-based models (i.e., GWR, TWR, and GTWR) showed great advantages over OLS in terms of higher model R 2 and more desirable model residuals, especially TWR and GTWR. The GWR, LMM, TWR, and GTWR improved the model explanation power by 3%, 5%, 12%, and 12%, respectively, from the R 2 (0.85) of OLS. TWR yielded slightly better model performance than GTWR and reduced the root mean squared errors (RMSE) and mean absolute error (MAE) of the model residuals by 67% compared with OLS; while GWR only reduced RMSE and MAE by 15% against OLS. LMM performed slightly better than GWR by accounting for both temporal autocorrelation between observations over time and spatial heterogeneity across the 13 cities under study, which provided an alternative for modeling PM 2.5 . Conclusions: The traditional OLS and GWR are inadequate for describing the non-stationarity of PM 2.5 . The temporal dependence was more important and significant than spatial heterogeneity in our data. Our study provided evidence of spatial–temporal heterogeneity and possible solutions for modeling the relationships between PM 2.5 and 5 criteria air pollutants for Heilongjiang province, China.