Table 3.

Performance measures for mis-specified logit models fitted to 100 simulated data sets with 4-fold fully out-of-sample cross validation: Using an exponential function for Gaussian spatial correlation.

		Scenario 1					Scenario 2
		TV	AE	PB	CR	MSE	TV	AE	PB	CR	MSE
β0	Standard Multilevel	−0.5	−0.3	−31.5	0.5	0.9	−0.5	−0.4	−23.1	0.5	0.5
	Pure Spatiala	−0.5	−0.3	−37.5	0.9	1.1	−0.5	−0.4	−18.0	0.9	0.5
	Hybrid CAR	−0.5	−0.4	−29.4	0.4	1.0	−0.5	−0.4	−21.7	0.4	0.5
	Hybrid Spatiala	−0.5	−0.3	−43.7	0.9	1.7	−0.5	−0.3	−31.5	0.9	1.1
β1	Standard Multilevel	0.8	0.7	−12.9	0.8	0.0	0.8	0.7	−13.5	0.7	0.0
	Pure Spatial	0.8	0.7	−12.9	0.7	0.0	0.8	0.7	−13.6	0.7	0.0
	Hybrid CAR	0.8	0.7	−12.1	0.8	0.0	0.8	0.7	−13.0	0.8	0.0
	Hybrid Spatial	0.8	0.7	−12.8	0.7	0.0	0.8	0.7	−13.4	0.7	0.0
γ1	Standard Multilevel	−0.5	−0.4	−15.5	1.0	0.1	−0.5	−0.5	−6.9	1.0	0.1
	Pure Spatial	−0.5	−0.4	−18.5	1.0	0.1	−0.5	−0.5	−8.6	0.9	0.1
	Hybrid CAR	−0.5	−0.4	−15.5	1.0	0.1	−0.5	−0.5	−5.2	1.0	0.1
	Hybrid Spatial	−0.5	−0.4	−17.8	1.0	0.1	−0.5	−0.5	−7.2	1.0	0.1
${\sigma }_u^2$	Standard Multilevel	3.0	4.1	38.2	0.7	3.6	3.0	3.2	7.9	0.9	1.3
	Hybrid CAR	3.0	2.1	−31.6	0.8	3.8	3.0	2.0	−33.0	0.8	3.2
	Hybrid Spatial	3.0	1.6	−45.0	0.7	2.5	3.0	1.7	−42.9	0.7	2.2
${\sigma }_s^2$	Pure Spatial	3.0	7.2	141.2	0.7	40.4	1.5	4.8	223.1	0.1	18.4
	Hybrid CAR	3.0	9.7	221.8	0.7	71.8	1.5	6.4	326.8	0.8	43.4
	Hybrid Spatial	3.0	6.7	123.6	1.0	41.3	1.5	4.2	183.2	1.0	25.3
ϕ	Pure Spatial	$\sqrt{3}$	5.8	235.5	0.6	19.8	$\sqrt{3}$	6.8	294.5	0.4	27.7
	Hybrid Spatial	$\sqrt{3}$	3.7	111.7	1.0	5.5	$\sqrt{3}$	4.2	144.6	1.0	7.6

		Scenario 3					Scenario 4
		TV	AE	PB	CR	MSE	TV	AE	PB	CR	MSE
β0	Standard Multilevel	−0.5	−0.3	−35.5	0.6	0.7	−0.5	−0.4	−23.9	0.6	0.3
	Pure Spatiala	−0.5	−0.4	−17.7	0.9	1.0	−0.5	−0.4	−16.2	1.0	0.5
	Hybrid CAR	−0.5	−0.3	−33.6	0.4	0.7	−0.5	−0.4	−22.8	0.6	0.4
	Hybrid Spatiala	−0.5	−0.4	−17.1	1.0	1.5	−0.5	−0.4	−27.0	0.9	0.7
β1	Standard Multilevel	0.8	0.7	−13.3	0.7	0.0	0.8	0.7	−13.6	0.7	0.0
	Pure Spatial	0.8	0.7	−13.3	0.7	0.0	0.8	0.7	−13.7	0.7	0.0
	Hybrid CAR	0.8	0.7	−12.4	0.8	0.0	0.8	0.7	−13.1	0.8	0.0
	Hybrid Spatial	0.8	0.7	−13.1	0.7	0.0	0.8	0.7	−13.5	0.7	0.0
γ1	Standard Multilevel	−0.5	−0.4	−18.7	0.9	0.1	−0.5	−0.4	−17.9	1.0	0.1
	Pure Spatial	−0.5	−0.4	−19.2	0.9	0.1	−0.5	−0.4	−18.3	0.9	0.1
	Hybrid CAR	−0.5	−0.4	−15.7	1.0	0.1	−0.5	−0.4	−16.6	1.0	0.1
	Hybrid Spatial	−0.5	−0.4	−17.8	0.9	0.1	−0.5	−0.4	−17.5	0.9	0.1
${\sigma }_u^2$	Standard Multilevel	3.0	4.3	44.5	0.8	3.9	3.0	3.4	13.1	0.9	1.0
	Hybrid CAR	3.0	2.2	−27.2	0.9	4.1	3.0	2.0	−32.1	0.8	1.5
	Hybrid Spatial	3.0	1.4	−51.9	0.7	2.9	3.0	1.7	−42.6	0.8	2.2
${\sigma }_s^2$	Pure Spatial	3.0	7.6	152.4	0.7	39.5	1.5	5.2	246.4	0.1	20.5
	Hybrid CAR	3.0	10.9	262.0	0.7	99.8	1.5	6.8	353.7	0.8	38.2
	Hybrid Spatial	3.0	7.4	145.5	0.9	45.6	1.5	4.1	173.6	1.0	17.9
ϕ	Pure Spatial	$\sqrt{6}$	5.5	125.7	0.8	12.1	$\sqrt{6}$	6.7	174.3	0.6	19.8
	Hybrid Spatial	$\sqrt{6}$	3.8	55.0	1.0	3.2	$\sqrt{6}$	4.4	80.4	1.0	5.0

Note: TV = true value; AE = average estimate; PB = percentage bias; CR = coverage rate with 95% credible interval; MSE = mean square error.

^aExponential spatial correlation function.