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Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 2 Growth curve model coefficient and variation estimates for the sample of female students in high poverty schools

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

47.75

15.00

− 0.74

3.94

0.05

1.20

− 0.11

87.64

1.30

1.29

7.68

47.91

BLR Pooling

32.90

14.52

− 0.61

3.37

0.17

1.04

− 0.05

87.61

0.53

2.85

105.69

55.52

BLR AGDP

50.64

13.73

− 0.61

3.82

0.03

0.30

− 0.01

88.29

1.32

1.28

7.45

48.58

PP (0.25)

34.85

14.83

− 0.67

3.60

0.15

1.13

− 0.07

84.13

1.67

1.85

76.06

54.23

PP (0.5)

33.31

14.76

− 0.64

3.44

0.16

1.11

− 0.06

85.36

1.12

2.46

95.75

54.49

PP (0.75)

33.08

14.64

− 0.62

3.39

0.16

1.07

− 0.06

86.75

0.76

2.72

102.90

55.00

BDB IG(1,1) W2,W2

47.64

15.00

− 0.74

3.94

0.05

1.20

− 0.11

85.52

1.69

1.19

7.23

54.22

BDB IG(1,0.001) W2,W2

48.11

14.94

− 0.73

3.88

0.05

1.14

− 0.10

85.35

1.69

1.20

7.47

54.22

BDB IG(1,1) W2,W20

47.48

15.01

− 0.74

3.93

0.05

1.20

− 0.11

85.20

1.71

1.19

7.32

54.25

BDB IG(1,.001) W2,W20

47.75

14.95

− 0.74

3.82

0.05

1.15

− 0.10

85.28

1.70

1.19

7.24

54.23

BDB IG(1,1) W20,W2

47.60

15.00

− 0.74

3.94

0.05

1.20

− 0.11

84.96

1.70

1.23

7.26

54.20

BDB IG(1,.001) W20,W2

47.76

14.94

− 0.73

3.88

0.05

1.14

− 0.10

84.91

1.70

1.23

7.64

54.19

BDB IG(1,1) W20,W20

47.60

14.99

− 0.74

3.92

0.05

1.19

− 0.11

85.22

1.68

1.23

6.95

54.20

BDB IG(1,.001) W20,W20

48.02

14.94

− 0.73

3.87

0.05

1.14

− 0.10

85.33

1.67

1.23

6.87

54.16

CP W2,W2

48.12

14.96

− 0.74

3.81

0.05

1.17

− 0.10

85.02

1.74

1.18

6.58

54.25

  1. 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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