Table 5.

Posterior statistics of the parameters for scenarios A and B in Sect. 4.1

Scen.	Parameter	True value	Mean	SD	95% CI
A1	${\psi }_{11}$	0.5	1.38	1.02	(0.08, 3.91)
	${\psi }_{12}$	0.25	0.38	0.28	(0.02, 1.15)
	${\psi }_{21}$	6	5.84	0.92	(4.18, 7.81)
	${\psi }_{22}$	− 0.25	−  0.27	0.11	(− 0.50, − 0.06)
	${\psi }_{31}$	0.5	0.60	0.25	(0.22, 1.04)
A2	${\psi }_{11}$	2.50	3.07	2.31	(0.16, 8.79)
	${\psi }_{12}$	1.25	1.45	0.29	(0.94, 2.10)
	${\psi }_{21}$	30.00	29.86	2.63	(24.83, 35.13)
	${\psi }_{22}$	− 1.25	−  1.20	0.30	(− 1.78, − 0.64)
	${\psi }_{31}$	2.50	2.35	0.35	(1.71, 3.07)
A3	${\psi }_{11}$	10	13.75	6.67	(2.47, 27.43)
	${\psi }_{12}$	5	4.50	0.52	(3.41, 5.45)
	${\psi }_{21}$	120	119.15	5.37	(108.83, 129.65)
	${\psi }_{22}$	− 5	− 4.68	0.60	(− 5.85, − 3.50)
	${\psi }_{31}$	10	9.03	0.64	(7.82, 10.31)
A4	${\psi }_{11}$	50	40.81	13.65	(19.79, 67.81)
	${\psi }_{12}$	25	24.69	0.94	(22.83, 26.46)
	${\psi }_{21}$	600	597.80	11.89	(574.64, 621.42)
	${\psi }_{22}$	− 25	− 24.88	1.30	(− 27.45, − 22.31)
	${\psi }_{31}$	50	47.66	1.47	(44.83, 50.59)
A5	${\psi }_{11}$	150	202.53	24.65	(129.16, 240.98)
	${\psi }_{12}$	75	72.54	1.84	(68.95, 76.17)
	${\psi }_{21}$	1800	1800.26	20.91	(1759.32, 1840.96)
	${\psi }_{22}$	− 75	− 76.16	2.29	(− 80.55, − 71.65)
	${\psi }_{31}$	150	144.11	2.48	(139.27, 149.01)
B1	${\psi }_{11}$	1.7	2.07	0.97	(0.78, 4.81)
	${\psi }_{12}$	0.85	0.86	0.07	(0.72, 0.98)
	${\psi }_{21}$	20.4	19.47	1.15	(17.20, 21.68)
	${\psi }_{22}$	− 0.85	− 0.79	0.10	(− 0.97, − 0.57)
	${\psi }_{31}$	1.7	1.50	0.21	(1.11, 1.95)
	${\theta }_1$	0.066	0.07	0.03	(0.02, 0.14)
	${\theta }_2$	0.066	0.09	0.04	(0.03, 0.17)
	${\theta }_3$	0.066	0.07	0.05	(0.01, 0.20)
	$({\theta }_{11},{\theta }_{12},{\theta }_{13})$	(1/3, 1/3, 1/3)	(0.24, 0.50, 0.26)	(0.16, 0.18, 0.17)	–
	$({\theta }_{21},{\theta }_{22},{\theta }_{23})$	(1/3, 1/3, 1/3)	(0.39, 0.32, 0.29)	(0.22, 0.17, 0.20)	–
	$({\theta }_{31},{\theta }_{32})$	(0.5, 0.5)	(0.71, 0.29)	(0.22, 0.22)	–
B2	${\psi }_{11}$	1	1.15	0.52	(0.44, 2.57)
	${\psi }_{12}$	0.5	0.49	0.03	(0.43, 0.55)
	${\psi }_{21}$	12	11.68	0.67	(10.36, 12.96)
	${\psi }_{22}$	− 0.5	− 0.47	0.06	(− 0.59, − 0.35)
	${\psi }_{31}$	1	1.07	0.12	(0.84, 1.29)
	${\theta }_1$	0.066	0.07	0.02	(0.03, 0.13)
	${\theta }_2$	0.066	0.08	0.03	(0.03, 0.15)
	${\theta }_3$	0.066	0.09	0.04	(0.04, 0.19)
	$({\theta }_{11},{\theta }_{12},{\theta }_{13})$	(1/3, 1/3, 1/3)	(0.23, 0.22, 0.55)	(0.15, 0.13, 0.17)	–
	$({\theta }_{21},{\theta }_{22},{\theta }_{23})$	(1/3, 1/3, 1/3)	(0.37,0.25,0.38)	(0.21, 0.16, 0.21)	–
	$({\theta }_{31},{\theta }_{32})$	(0.5, 0.5)	(0.72, 0.28)	(0.16, 0.16)	–
B3	${\psi }_{11}$	0.5	0.68	0.22	(0.29, 1.15)
	${\psi }_{12}$	0.25	0.25	0.02	(0.20, 0.29)
	${\psi }_{21}$	6	5.88	0.26	(5.39, 6.39)
	${\psi }_{22}$	− 0.25	- 0.24	0.02	(− 0.28, − 0.20)
	${\psi }_{31}$	0.5	0.43	0.06	(0.32, 0.54)
	${\theta }_1$	0.066	0.09	0.02	(0.05, 0.15)
	${\theta }_2$	0.066	0.09	0.02	(0.05, 0.13)
	${\theta }_3$	0.066	0.07	0.03	(0.03, 0.14)
	$({\theta }_{11},{\theta }_{12},{\theta }_{13})$	(1/3, 1/3, 1/3)	(0.12, 0.47, 0.41)	(0.09, 0.14, 0.14)	–
	$({\theta }_{21},{\theta }_{22},{\theta }_{23})$	(1/3, 1/3, 1/3)	(0.55, 0.25, 0.20)	(0.17, 0.14, 0.14)	–
	$({\theta }_{31},{\theta }_{32})$	(0.5, 0.5)	(0.67, 0.33)	(0.18, 0.18)	–