Table 2.

Results from simulation study comparing bivariate CAR and separate CAR Poisson hurdle models (n = 100 simulated datasets). Parameter estimates and biases for β₂₁ are highlighted in bold.

			Posterior estimates
			Correlated model			Separate model
ρ	Model Parameter	True Value	Posterior Mean	Bias	MSE	Posterior Mean	Bias	MSE
0	β11	−1	−1.01	−0.01	0.007	−1.004	−0.004	0.007
	β12	1	1.01	0.01	0.002	1.01	0.01	0.002
	β21	2	2.004	0.004	0.004	1.996	−0.004	0.004
	β22	−1	−1.001	−0.001	<0.001	−1.001	−0.001	<0.001
	Σ11	4	3.996	−0.004	0.46	4.17	0.17	0.54
	Σ12	0	−0.013	−0.013	0.85	—	—	—
	Σ22	16	15.60	−0.40	4.59	16.04	0.04	4.87
0.25	β11	−1	−1.01	−0.01	0.005	−1.01	−0.01	0.005
	β12	1	1.01	0.01	0.002	1.01	0.01	0.002
	β21	2	2.01	0.01	0.004	2.02	0.02	0.004
	β22	−1	−0.999	0.001	<0.001	−0.999	0.001	<0.001
	Σ11	4	3.996	−0.004	0.52	4.18	0.18	0.62
	Σ12	2	1.92	−0.08	0.92	—	—	—
	Σ22	16	15.75	−0.25	3.72	15.91	−0.09	3.86
0.50	β11	−1	−1.01	−0.01	0.006	−1.002	−0.002	0.006
	β12	1	1.01	0.01	0.002	1.01	0.01	0.002
	β21	2	2.03	0.01	0.005	2.05	0.05	0.008
	β22	−1	−1.002	−0.002	<0.001	−1.002	−0.002	<0.001
	Σ11	4	4.06	0.06	0.70	4.18	0.18	0.86
	Σ12	4	4.02	0.02	0.84	—	—	—
	Σ22	16	15.65	−0.35	4.56	15.45	−0.55	4.97
0.75	β11	−1	−1.01	− 0.01	0.007	−0.99	0.01	0.007
	β12	1	1.01	0.01	0.002	0.99	−0.01	0.002
	β21	2	2.01	0.01	0.006	2.09	0.09	0.01
	β22	−1	−1.001	−0.001	<0.001	−1.001	−0.001	<0.001
	Σ11	4	4.11	0.11	0.68	4.31	0.31	0.93
	Σ12	6	6.16	0.16	1.70	—	—	—
	Σ22	16	15.92	−0.08	7.03	14.67	−1.33	6.69