Table 2.

(a) Median absolute deviation (MAD) × 100 for the simulation study. MAD is averaged across all 50 locations for each pollutant. The overall average over datasets is presented here. Simulation settings for α_k, π_k are shown in columns 2 and 3, and abbreviated names of the components used to generate the response are in column 1. A “*” indicates a statistically significant difference from the SpVS model. (b) Power and Type-I error for spatial model with no variable selection (Sp), exchangeable variable selection model (EVS), and spatial variable selection model (SpVS) for local and global covariates. We calculate power for each setting of the true value of α_k.

(a) Median absolute deviation (MAD)
			Independent			Weak correlation			Strong correlation
	α × 100	π	Sp	EVS	SpVS	Sp	EVS	SpVS	Sp	EVS	SpVS
Sulf.	5	1	1.39*	1.66*	1.48	1.36	1.65*	1.38	1.10	1.55*	1.12
Nitr.	10	1	1.40*	1.46	1.45	1.37*	1.59*	1.41	1.16	1.43*	1.14
Sili.	5	0.3	1.34*	0.91	0.95	1.41*	0.99*	1.11	1.17*	0.95	0.91
El C.	5	0.7	1.91*	2.10	2.08	1.79	2.04*	1.78	1.49*	1.83*	1.44
Sodi.	10	0.3	1.53*	0.80	0.86	1.52*	0.79	0.84	1.21*	0.70	0.66
Or C.	10	0.7	2.30*	2.02	2.04	2.30*	2.01	1.95	1.91*	2.05*	1.60
Arse.	0	0	0.53*	0.12	0.12	0.50*	0.16	0.19	0.46*	0.13*	0.18
Brom.	0	0	0.60*	0.15	0.13	0.56*	0.14*	0.21	0.50*	0.12*	0.24
Calc.	0	0	0.63*	0.15	0.15	0.69*	0.15*	0.25	0.54*	0.12*	0.26
Avg. local, βk(s) = 0			1.61*	1.19*	1.23	1.64*	1.24	1.24	1.26*	0.72	0.63
Avg. local, βk(s) ≠ 0			1.93*	1.72	1.73	1.87*	1.67*	1.59	1.62	2.04	1.67

(b) Power and Type I error
		Independent			Weak correlation			Strong correlation
	α k	Sp	EVS	SpVS	Sp	EVS	SpVS	Sp	EVS	SpVS
					Power
Local	0.05	0.41	0.30	0.34	0.48	0.31	0.49	0.65	0.37	0.67
Local	0.10	0.80	0.76	0.75	0.84	0.74	0.81	0.90	0.77	0.91
Global	0.05	0.74	0.55	0.61	0.75	0.55	0.73	0.85	0.57	0.85
Global	0.10	1.00	0.92	0.92	0.99	0.88	0.95	1.00	0.90	0.99
					Type-I Error
Local		0.03	0.01	0.02	0.05	0.01	0.07	0.06	0.01	0.08
Global		0.01	0.00	0.00	0.00	0.00	0.01	0.01	0.00	0.01