Table 4.

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

Cycle	Method${}^1$	TCSHORT		STRATIO		FEMALE:TCSHORT
		Mean	SD	Mean	SD	Mean	SD
2003	BLR non inf	$-$12.50	3.35	$-$0.76	0.52	0.09	2.80
2006	BLR non inf	$-$0.89	3.41	$-$0.24	0.65	$-$2.87	2.27
2009	BLR non inf	$-$16.28	4.07	$-$1.27	0.61	$-$0.15	2.64
2012	BLR non inf	$-$13.15	3.61	0.06	0.31	0.93	2.45
2015	BLR non inf	$-$5.68	2.94	0.03	0.60	$-$1.31	2.09
2018	BLR non inf	$-$8.40	3.18	0.33	0.29	1.85	2.52
	BLR inf	$-$9.19	2.29	0.15	0.25	0.76	1.74
	BLR pooling	$-$9.60	1.39	$-$0.11	0.18	$-$0.08	0.96
	BDB IG(1,1) W2	$-$8.43	3.16	0.34	0.29	1.80	2.40
	BDB IG(1,.1) W2	$-$8.80	3.49	0.32	0.28	1.79	2.36
	BDB IG(1,.001) W2	$-$8.63	2.48	0.17	0.26	0.96	1.91
	BDB IG(1,1) W20	$-$8.41	3.22	0.34	0.29	1.78	2.40
	BDB IG(1,.1) W20	$-$8.42	3.14	0.34	0.29	1.81	2.37
	BDB IG(1,.001) W20	$-$8.66	2.51	0.17	0.26	0.97	1.93
	PP (.25)	$-$9.11	1.49	0.02	0.16	0.81	1.65
	PP (.5)	$-$9.39	1.40	$-$0.06	0.17	0.29	1.28
	PP (.75)	$-$9.54	1.38	$-$0.09	0.17	0.06	1.09

${}^1$BLR non inf: Bayesian linear regression with non-informative priors; BLR inf: Bayesian linear regression with informative priors; 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.