Environmental Science & Technology Table 1. Model Performance Statistics for GSH OP and PM10 Models pollu- tant GSH OP PM10 grouping across all by season by year by urban volu- metric densityc by site type annual- meand spatiale temporale across all by season by year by urban volu- metric densityc by site type annual- meand spatiale temporale urban background 0.45 0.44 winter 0.25 2002 0.39 low 0.34 0.67 0.73 0.71 0.83 winter 0.85 2002 0.68 low 0.74 0.67 0.61 0.76 cross-validation R2a 2004 0.41 2004 0.79 spring 0.34 2003 0.48 medium 0.50 roadside 0.36 spring 0.86 2003 0.92 medium 0.82 summer 0.39 2005 0.47 high 0.42 kerbside 0.13 summer 0.81 2005 0.78 high 0.87 0.78 autumn 0.34 2006 0.34 autumn 0.73 2006 0.73 urban background 0.25 0.29 winter 0.30 2002 0.30 low 0.31 0.14 0.13 0.12 4.62 winter 4.24 2002 4.68 low 5.51 2.68 2.65 2.16 spring 0.28 2003 0.25 medium 0.27 roadside 0.32 spring 5.15 2003 4.74 medium 4.73 RMSPEab 2004 0.29 2004 4.30 summer 0.29 2005 0.29 high 0.30 curbside 0.31 summer 4.12 2005 4.16 high 4.27 5.74 Article autumn 0.32 2006 0.31 autumn 4.56 2006 4.93 urban background 0.88 suburban roadside curbside 0.90 0.80 urban background 3.64 suburban roadside curbside 3.43 4.99 aAcross weekly averages (2118 at 34 locations for GSH OP and 12 041 at 66 locations for PM10). For PM10, two high values at two sites were removed as outliers. bRMSPE is root mean squared prediction error. Units are OP μg−1 for GSH OP and μg m−3 for PM10. c Deﬁned using tertiles of the urban volumetric density (see text for deﬁnition) within 500 m. For PM10, across only 6710 weekly averages at the 34 locations where GSH OP was also measured. dTo calculate “annual-mean” values, measurements and predictions were averaged by year at each site with at least 31 weeks of data per year. eTo calculate “spatial” values, measurements and predictions were averaged over time at each site with at least 40 weeks of data; similarly “temporal” refers to averaging over locations for all weeks for which measurements were available. 1.78, respectively, and an arithmetic standard deviation (SD) of 0.39. Weekly average PM10 levels in units of μg m−3 were approximately log-normally distributed, with 0%, 25%, 50%, geometric mean, 75%, and 100% values of 8.2, 20.3, 25.7, 26.0, 32.8, and 101.3, respectively, and a geometric SD of 1.43. GSH OP. Upon inclusion in univariate models, nine of the 10 GIS predictors identiﬁed in preliminary linear mixed eﬀect models improved predictive accuracy compared to the referent model (listed in Supporting Information Table S1), which included only the intercept, α, and the smooth term for time trend, h(t), as ﬁxed eﬀects. Interestingly, the inclusion of a smooth spatial term, g(si), decreased predictive accuracy and was not included. Thus, the model relied upon geographic covariates to explain spatial variation in GSH OP. Nonlinear spline terms did not increase predictive accuracy for any of the GIS covariates; therefore, linear eﬀects were used. In multivariable models, only NOX tailpipe emissions from heavy-goods vehicles within 50 m (NOXHGV50) and PM10 brake and tire wear emissions from all vehicles within 50 m (PM10BT50) remained signiﬁcant and maximized CV perform- ance. We then investigated the spatial scale over which the impacts of both of these covariates varied by using larger buﬀers of 100 m instead of 50 m. For PM10BT50, the original 50 m buﬀer performed best (CV R2 = 0.42 for 50 m vs 0.39 for 100 m), whereas for NOXHGV50 a 100 m buﬀer (NOXHGV100) performed slightly better than the 50 m buﬀer (CV R2 = 0.424 for 100 m vs 0.417 for 50 m). Allowing the linear slope to change seasonally further improved predictive accuracy slightly (Supporting Information Table S1; CV R2 = 0.44 with seasonal interaction and 0.42 without) for PM10BT50, but did not for NOXHGV100 (data not shown). Thus, the ﬁnal GSH OP prediction model was of the following form: 7615 dx.doi.org/10.1021/es3010305 | Environ. Sci. Technol. 2012, 46, 7612−7620