Table 2. Performance of PM_2.5 Composition Models to Assess within-Area Variation: Average within-Area r^2a.

avg. WA r2	inclusion of X, Y coordinates	evaluation method	Cu	Fe	K	Ni	S	Si	V	Zn
SLR	one-step	five-fold HOV	0.34	0.35	0.09	0.18	0.14	0.18	0.21	0.20
		LOAOCV	0.37	0.38	0.09	0.15	0.22	0.21	0.23	0.18
	two-step, step1	five-fold HOV	0.34	0.34	0.08	0.17	0.14	0.20	0.18	0.21
		LOAOCV	0.35	0.35	0.09	0.15	0.22	0.20	0.20	0.18
	two-step, step2	five-fold HOV	0.35	0.36	0.07	0.17	0.14	0.20	0.19	0.19
		LOAOCV	0.36	0.36	0.09	0.15	0.22	0.20	0.21	0.18
RF	one-step	five-fold HOV	0.31	0.31	0.05	0.21	0.21	0.19	0.27	0.24
		LOAOCV	0.35	0.35	0.12	0.18	0.21	0.17	0.27	0.18
	two-step, step1	five-fold HOV	0.31	0.30	0.06	0.21	0.22	0.17	0.27	0.24
		LOAOCV	0.34	0.34	0.07	0.16	0.21	0.16	0.23	0.19
	two-step, step2	five-fold HOV	0.29	0.29	0.07	0.21	0.23	0.17	0.29	0.25
		LOAOCV	0.34	0.34	0.07	0.16	0.21	0.16	0.23	0.20

^aSLR = supervised linear regression; RF = random forest; r² = squared Pearson correlation; avg. WA r² is the average of 19 study area-specific r²s (area-specific r²s evaluated by five-fold HOV are shown in Figure S4); HOV = hold-out validation; LOAOCV = leave-one-area-out cross-validation.