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

Table 2 Estimation of the ecological link β when ${\bar{E}}_{h}$ = 23.35 and ρ_xx= 0.0, 0.4 (400 replications)

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⁾
0.0	0.00	M ₀	0.000	1.63			1.73	1.73	0.953	0.047
		BYM	0.000	1.76			1.74	1.73	0.958	0.042
	0.12	M ₀	0.119	1.61	-0.44	0.69	1.67	1.67	0.930	1.000
		BYM	0.120	1.72	-0.31	0.70	1.68	1.68	0.955	1.000
	0.21	M ₀	0.210	1.60	0.49	0.39	1.64	1.64	0.948	1.000
		BYM	0.210	1.72	0.58	0.39	1.66	1.66	0.960	1.000
	0.33	M ₀	0.329	1.57	-0.28	0.23	1.58	1.58	0.953	1.000
		BYM	0.329	1.70	-0.24	0.24	1.58	1.58	0.968	1.000
0.4	0.00	M ₀	-0.001	1.72			1.76	1.76	0.955	0.045*
		BYM	-0.001	1.90			1.78	1.78	0.975	0.025
	0.12	M ₀	0.121	1.73	0.79	0.73	1.75	1.75	0.945	1.000
		BYM	0.121	1.91	0.78	0.74	1.78	1.78	0.968	1.000
	0.21	M ₀	0.211	1.72	0.41	0.39	1.66	1.66	0.958	1.000
		BYM	0.211	1.90	0.50	0.39	1.67	1.67	0.973	1.000
	0.33	M ₀	0.332	1.70	0.71	0.25	1.68	1.69	0.945	1.000
		BYM	0.332	1.89	0.70	0.25	1.70	1.71	0.973	1.000

⁽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.

ISSN: 1476-072X