International Journal of Health Geographics

Table 3 Estimation of the ecological link β when ${\bar{E}}_{h}$ = 23.35 and ρ_xx= 0.90, 0.95, 0.98

From: Robustness of the BYM model in absence of spatial variation in the residuals

(1)(2)(3)(4)(5)(6)(7)(8)(*)
ρ _xx ⁽¹⁾	β	Model	$\bar{β}$ _sim ⁽²⁾	${\bar{σ}}_{β_{s i m}}$	MB⁽⁴⁾	sd(MB)	sd(β_sim)⁽⁵⁾	RMSE⁽⁶⁾	π(β)⁽⁷⁾	1 - π(0)⁽⁸⁾
0.90	0.00	M ₀	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	M ₀	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	M ₀	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	M ₀	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	M ₀	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	M ₀	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	M ₀	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	M ₀	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	M ₀	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	M ₀	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	M ₀	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	M ₀	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⁾ $\bar{β}$ _sim: 100 * mean of posterior means
⁽³⁾ ${\bar{σ}}_{β_{s i m}}$ : 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.

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ISSN: 1476-072X

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