Table 3.

Estimation of the ecological link β when ${\overline{E}}_h$ = 23.35 and ρ_xx = 0.90, 0.95, 0.98

(1)(2)(3)(4)(5)(6)(7)(8)(*)
ρxx(1)	β	Model	$\overline{\beta }$sim(2)	${\overline{\sigma }}_{{\beta }_{sim}}$	MB(4)	sd(MB)	sd(βsim)(5)	RMSE(6)	π(β)(7)	1 - π(0)(8)
0.90	0.00	M0	0.003	2.96			2.98	2.99	0.945	0.055*
		BYM	0.003	3.39			3.03	3.04	0.970	0.030
	0.12	M0	0.122	2.98	2.07	1.24	2.99	3.00	0.958	0.973*
		BYM	0.123	3.44	2.51	1.27	3.07	3.08	0.973	0.938
	0.21	M0	0.213	2.96	1.38	0.79	3.32	3.34	0.930	0.998
		BYM	0.213	3.41	1.31	0.81	3.41	3.42	0.955	0.998
	0.33	M0	0.331	2.98	0.37	0.47	3.11	3.11	0.943	1.000
		BYM	0.331	3.43	0.39	0.47	3.13	3.13	0.965	1.000
0.95	0.00	M0	0.002	4.07			4.04	4.04	0.950	0.050*
		BYM	0.002	4.72			4.14	4.14	0.975	0.025
	0.12	M0	0.121	4.05	1.03	1.82	4.38	4.37	0.945	0.843*
		BYM	0.121	4.70	1.18	1.89	4.54	4.54	0.960	0.775
	0.21	M0	0.208	3.99	-1.07	0.99	4.18	4.18	0.960	0.988
		BYM	0.208	4.62	-0.80	1.03	4.31	4.31	0.978	0.983
	0.33	M0	0.333	4.16	0.78	0.66	4.33	4.33	0.963	1.000
		BYM	0.333	4.80	0.98	0.66	4.34	4.35	0.980	1.000
0.98	0.00	M0	0.002	6.29			6.48	6.48	0.950	0.050*
		BYM	0.002	7.29			6.53	6.53	0.970	0.030
	0.12	M0	0.121	6.23	1.22	2.49	5.98	5.98	0.953	0.545*
		BYM	0.122	7.20	1.26	2.47	5.99	5.98	0.975	0.420
	0.21	M0	0.207	6.35	-1.36	1.57	6.61	6.60	0.960	0.845*
		BYM	0.207	7.35	-1.39	1.59	6.67	6.67	0.985	0.782
	0.33	M0	0.330	6.27	0.09	1.00	6.64	6.63	0.935	0.985
		BYM	0.331	7.28	0.24	1.01	6.69	6.68	0.975	0.978

⁽¹⁾ ρ_xx : autocorrelation at 100 km

⁽²⁾ $\overline{\beta }$_sim : 100 * mean of posterior means

⁽³⁾ ${\overline{\sigma }}_{{\beta }_{sim}}$ : 100 * mean of posterior standard deviations

⁽⁴⁾ MB : 100 * Mean Bias

⁽⁵⁾ sd(β_sim) : 100 * standard deviation of posterior means

⁽⁶⁾ RMSE : 100 * Root Mean Square Error

⁽⁷⁾ π(β) : Coverage proportion β ∈ CI(β)

⁽⁸⁾ 1 - π(0) : Non-Coverage proportion 0 ∉ CI(β)

^(*) : Indicator of p-value < 5% from McNemar's test (1)(2)(3) for comparing proportions 1 - π(0) under M₀ and BYM models.