Table 4.

Estimation of the ecological link β when ^ρ_xx = 0.95 while ${\overline{E}}_h$ varying

(1)(2)(3)(4)(5)(6)(7)(8)(*)
${\overline{E}}_h$	β	Model	$\overline{\beta }$sim(1)	${\overline{\sigma }}_{{\beta }_{sim}}$	MB(3)	sd(MB)	sd(βsim)(4)	RMSE(5)	π(β)(6)	1 - π(0)(7)
46.6	0.00	M0	-0.001	2.84			2.76	2.76	0.958	0.042*
		BYM	-0.001	3.40			2.85	2.85	0.975	0.025
	0.12	M0	0.118	2.81	-1.34	1.21	2.91	2.91	0.945	0.960*
		BYM	0.119	3.38	-1.18	1.21	2.91	2.91	0.980	0.930
	0.21	M0	0.212	2.87	0.94	0.69	2.89	2.89	0.955	1.000
		BYM	0.212	3.47	0.75	0.70	2.95	2.96	0.983	1.000
	0.33	M0	0.329	2.88	-0.21	0.47	3.10	3.10	0.953	1.000
		BYM	0.330	3.45	-0.08	0.48	3.19	3.19	0.980	1.000
23.3	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	4.34	0.963	1.000
		BYM	0.333	4.79	0.98	0.66	4.34	4.35	0.980	1.000
2.33	0.00	M0	0.007	12.4			13.5	13.4	0.935	0.065
		BYM	0.008	13.3			13.4	13.4	0.948	0.052
	0.12	M0	0.112	12.5	-6.94	5.38	12.9	12.9	0.953	0.162*
		BYM	0.113	13.4	-5.65	5.43	13.0	13.0	0.965	0.130
	0.21	M0	0.206	12.8	-1.92	3.45	14.5	14.5	0.927	0.410*
		BYM	0.206	13.8	-1.98	3.46	14.6	14.5	0.940	0.368
	0.33	M0	0.341	13.0	3.38	2.12	14.00	14.0	0.938	0.738*
		BYM	0.343	13.9	4.05	2.14	14.1	14.2	0.960	0.715

⁽¹⁾$\overline{\beta }$_sim : 100 * mean of posterior means

⁽²⁾${\overline{\sigma }}_{{\beta }_{sim}}$ : 100 * mean of posterior standard deviations

⁽³⁾ MB : 100 * Mean Bias

⁽⁴⁾ sd(β_sim) : 100 * standard deviation of posterior means

⁽⁵⁾ RMSE : 100 * Root Mean Square Error

⁽⁶⁾π(β) : Coverage proportion β ∈ CI(β)

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

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