. 2022 Jun 10;88(1):1–30. doi: 10.1007/s11336-022-09869-3

Table 3.

Posterior means and standard deviations (SD) of individual-level coefficients for case study 2 (multilevel model).

Cycle	Method $^{1}$	Intercept		FEMALE		PARED		HOMEPOS		IMMIG
Cycle	Method $^{1}$	Mean	SD	Mean	SD	Mean	SD	Mean	SD	Mean	SD
2003	BLR non inf	451.06	11.53	$-$ 9.77	2.59	2.56	0.54	26.36	1.39	3.52	4.15
2006	BLR non inf	421.04	13.19	$-$ 12.50	2.15	4.53	0.49	18.35	1.26	2.48	3.50
2009	BLR non inf	456.17	12.78	$-$ 16.23	2.49	3.25	0.49	19.42	1.33	3.13	3.26
2012	BLR non inf	433.41	9.61	$-$ 12.24	2.54	3.95	0.53	15.17	1.21	$-$ 10.14	3.46
2015	BLR non inf	422.29	12.09	$-$ 9.40	2.28	3.32	0.47	15.00	1.11	0.67	3.10
2018	BLR non inf	435.74	9.92	$-$ 7.82	2.57	3.29	0.57	19.55	1.26	$-$ 11.39	3.54
	BLR inf	435.28	7.69	$-$ 10.40	1.74	3.33	0.38	19.62	0.89	$-$ 6.05	2.54
	BLR pooling	434.32	4.33	$-$ 11.28	0.96	3.49	0.21	18.54	0.51	$-$ 1.89	1.41
	BDB IG(1,1) W2	435.93	9.72	$-$ 7.78	2.44	3.27	0.55	19.48	1.19	$-$ 11.29	3.46
	BDB IG(1,.1) W2	436.17	9.55	$-$ 7.79	2.46	3.25	0.55	19.42	1.19	$-$ 11.08	3.42
	BDB IG(1,.001) W2	437.26	8.53	$-$ 8.78	2.21	3.28	0.48	19.36	1.13	$-$ 9.39	3.26
	BDB IG(1,1) W20	435.90	9.92	$-$ 7.82	2.46	3.26	0.55	19.42	1.21	$-$ 11.26	3.47
	BDB IG(1,.1) W20	436.01	9.86	$-$ 7.80	2.44	3.26	0.55	19.41	1.19	$-$ 11.16	3.46
	BDB IG(1,.001) W20	437.39	8.50	$-$ 8.82	2.16	3.28	0.47	19.34	1.14	$-$ 9.34	3.26
	PP (.25)	426.05	5.74	$-$ 10.02	1.64	4.02	0.36	20.91	0.84	$-$ 3.87	2.28
	PP (.5)	430.96	4.98	$-$ 10.71	1.28	3.71	0.28	19.58	0.66	$-$ 2.61	1.87
	PP (.75)	433.14	4.48	$-$ 11.07	1.09	3.56	0.24	18.92	0.56	$-$ 2.14	1.59

$^{1}$ BLR non inf: Bayesian linear regression with non-informative prior; BLR inf: Bayesian linear regression with informative prior; BDB: Bayesian dynamic borrowing; IG: inverse-gamma prior for level-1 variance of the joint prior distribution, which determines the degree of level-1 borrowing; W2: Wishart prior with weak borrowing for level-2 precision matrix (results were converted back the covariance matrix); W20: Wishart prior with strong borrowing for level-2 precision matrix (results were converted back the covariance matrix); PP: power priors.