Bayesian historical borrowing with longitudinal large-scale assessments

Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 3 Prediction performance of different borrowing methods for the sample of female students in high poverty schools

	Theil inequ coef	Theil bias prop	Theil var prop	RMSE	KLD	LOOIC (Student)	LOOIC (School)
BLR Noninformative	0.03	0.01	0.11	9.93	0.07	33967.63	33621.26
BLR Pooling	0.03	0.01	0.06	8.72	0.02	34192.96	33837.50
BLR AGDP	0.03	0.01	0.12	8.81	0.03	34027.67	33692.09
PP (0.25)	0.03	0.01	0.09	8.91	0.03	34124.25	33794.19
PP (0.5)	0.03	0.01	0.07	8.83	0.02	34145.22	33802.78
PP (0.75)	0.03	0.01	0.06	8.78	0.02	34191.10	33838.18
BDB IG(1,1) W2,W2	0.03	0.01	0.13	9.89	0.07	34090.48	33779.65
BDB IG(1,0.001) W2,W2	0.03	0.01	0.13	9.83	0.07	34093.57	33788.90
BDB IG(1,1) W2,W20	0.03	0.01	0.13	9.90	0.07	34086.56	33796.26
BDB IG(1,0.001) W2,W20	0.03	0.01	0.13	9.85	0.07	34089.09	33784.94
BDB IG(1,1) W20,W2	0.03	0.01	0.13	9.90	0.07	34107.72	33780.68
BDB IG(1,0.001) W20,W2	0.03	0.01	0.13	9.84	0.07	34097.21	33777.34
BDB IG(1,1) W20,W20	0.03	0.01	0.13	9.91	0.07	34085.33	33784.04
BDB IG(1,0.001) W20,W20	0.03	0.01	0.13	9.84	0.07	34084.31	33770.53
CP W2,W2	0.03	0.01	0.13	9.84	0.07	34087.65	33786.41

Theil Inequ Coef: Theil’s inequaility coefficient; Theil Bias Prop: Theil’s bias proportion; Theil Var Prop: Theil’s variance proportion; RMSE: root mean squared error of the predicted reading score vs. observed reading score at the spring of 5th grade; KLD: Kullback-Leibler Divergence Score; LOOIC (Student): Leave-one-out cross validation information criterion with each student left out one at a time; LOOIC (School): Leave-one-out cross validation information criterion with each school left out one at a time; 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