Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 4 Growth curve model coefficient and variation estimates for the full sample of female students

From: Bayesian historical borrowing with longitudinal large-scale assessments

	Regression coefficients							Stu-level			Sch-level
	Intcp	t	\(t^2\)	SES	FLunch	\(t\times\) SES	\(t^2\times\) SES	Var(Intcp)	Cov(Intcp,t)	Var(t)	Var(Intcp)	Var(R)
BLR Noninformative	55.83	15.49	− 0.79	4.65	− 0.04	1.24	− 0.12	120.90	− 2.29	1.28	8.27	53.47
BLR Pooling	41.20	15.91	− 0.61	3.88	0.05	1.93	− 0.12	140.88	− 9.61	6.05	102.35	83.57
BLR AGDP	59.22	13.02	− 0.53	3.06	− 0.04	1.13	− 0.10	120.75	− 2.17	1.23	8.88	58.73
PP (0.25)	43.09	15.92	− 0.65	4.36	0.03	1.59	− 0.10	120.31	− 7.16	4.51	84.96	82.60
PP (0.5)	41.70	16.01	− 0.63	4.11	0.04	1.77	− 0.11	130.23	− 8.45	5.56	98.41	83.05
PP (0.75)	41.28	15.96	− 0.62	4.00	0.05	1.86	− 0.11	136.78	− 9.16	5.89	101.23	83.37
BDB IG(1,1) W2,W2	55.83	15.49	− 0.79	4.66	− 0.04	1.23	− 0.12	110.59	− 0.59	0.85	8.56	81.68
BDB IG(1,0.001) W2,W2	55.84	15.51	− 0.79	4.52	− 0.04	1.29	− 0.13	110.65	− 0.58	0.84	8.32	81.68
BDB IG(1,1) W2,W20	55.83	15.49	− 0.79	4.67	− 0.04	1.24	− 0.12	110.13	− 0.58	0.85	9.35	81.68
BDB IG(1,0.001) W2,W20	55.84	15.51	− 0.79	4.52	− 0.04	1.29	− 0.13	110.11	− 0.59	0.85	9.49	81.65
BDB IG(1,1) W20,W2	55.81	15.49	− 0.79	4.67	− 0.04	1.24	− 0.12	110.65	− 0.63	0.88	8.60	81.63
BDB IG(1,0.001) W20,W2	55.83	15.51	− 0.79	4.53	− 0.04	1.29	− 0.13	110.98	− 0.68	0.88	8.50	81.62
BDB IG(1,1) W20,W20	55.83	15.49	− 0.79	4.66	− 0.04	1.23	− 0.12	110.34	− 0.65	0.88	9.43	81.62
BDB IG(1,0.001) W20,W20	55.82	15.51	− 0.79	4.52	− 0.04	1.29	− 0.13	110.22	− 0.64	0.87	9.44	81.64
CP W2,W2	55.98	15.51	− 0.79	4.45	− 0.04	1.29	− 0.13	110.85	− 0.58	0.84	7.63	81.72

Intcp:intercept; t: time; Stu-Level: student-level; Sch-Level: school-level; Var(R): variance of time-level residual; BLR: Bayesian Linear Regression; AGDP: aggregated data-dependent prior; PP: power prior; BDB: Bayesian dynamic borrowing; IG: inverse-gamma prior for time-level variance of the joint prior distribution, which determines the degree of time-level borrowing; W2: Wishart prior with weak borrowing for student-level (the former) or school-level (the latter) precision matrix (results were converted back the covariance matrix); W20: Wishart prior with strong borrowing for student-level (the former) or school-level (the latter) precision matrix (results were converted back the covariance matrix); CP: commensurate prior

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