Table 1.

The estimates of the mean, standard error (SE), standard deviation (SD), and coverage probabilities (CP) of 95% credible intervals based on logistic regression (LR), the reduced model, and the proposed model assuming either conditional independence or conditional dependence. ARE is asymptotic relative efficiency of the proposed model with respect to the reduced model.

(a) Conditional independence
	True	β0	β1	β2	β3	p1	q1	p2	q2
	pars	0.310	0.006	−1.800	0.700	0.800	0.850	0.900	0.700
LR	Mean	0.599	0.004	-0.929	0.297
	SD	0.142	0.009	0.245	0.375
	SE	0.131	0.009	0.225	0.368
	CP	0.400	0.930	0.030	0.740
Reduced model	Mean	0.282	0.008	−1.932	0.635	0.812	0.849	0.894	0.690
	SD	0.222	0.012	0.501	0.436	0.064	0.042	0.037	0.052
	SE	0.327	0.013	0.537	0.478	0.072	0.052	0.048	0.066
	CP	0.990	0.950	0.950	0.980	0.980	0.990	0.990	0.980
Proposed model	Mean	0.288	0.007	−1.827	0.652	0.797	0.846	0.898	0.694
	SD	0.149	0.010	0.332	0.352	0.032	0.029	0.022	0.032
	SE	0.141	0.010	0.290	0.386	0.032	0.028	0.024	0.034
	CP	0.940	0.950	0.930	0.950	0.950	0.960	0.980	0.960
	ARE	5.378	1.690	3.429	1.533	5.062	3.449	4.000	3.768

(b) Conditional dependence
	True	β0	β1	β2	β3	p1	q1	p2	q2
	pars	0.310	0.006	−1.800	0.700	0.800	0.850	0.830	0.638
LR	Mean	0.552	0.004	−0.769	0.219
	SD	0.119	0.010	0.222	0.365
	SE	0.130	0.009	0.224	0.363
	CP	0.530	0.910	0.000	0.710
Reduced model	Mean	0.330	0.008	−1.910	0.677	0.798	0.845	0.825	0.631
	SD	0.290	0.018	0.656	0.641	0.076	0.055	0.047	0.065
	SE	0.338	0.019	0.717	0.714	0.091	0.065	0.055	0.068
	CP	0.990	0.920	0.980	0.940	0.980	0.970	0.940	0.980
Proposed model	Mean	0.278	0.008	−1.834	0.661	0.803	0.846	0.838	0.633
	SD	0.175	0.012	0.330	0.389	0.039	0.034	0.035	0.036
	SE	0.196	0.012	0.346	0.439	0.042	0.039	0.038	0.040
	CP	0.960	0.950	0.960	0.990	0.990	0.980	0.970	0.970
	ARE	2.974	2.507	4.294	2.645	4.694	2.778	2.095	2.890