Table 5 A summary of the fixed and random effects estimated from HLM models

School mean achievement, \({\upbeta }_{0}\)

 Intercept, \({\upgamma}_{00}\)

467.98 (6.27)

485.18 (3.63)

472.12 (5.96)

482.94 (3.53)

 M_ses, \({\upgamma}_{01}\)

–

33.82 (3.37)

–

29.11 (4.63)

 Instruction, \({\upgamma}_{02}\)

–

–

21.66 (7.46)

17.92 (4.96)

 Readiness, \({\upgamma}_{03}\)

–

–

12.42 (3.75)

7.39 (2.76)

 Condition, \({\upgamma}_{04}\)

–

–

7.40 (2.74)

.59 (2.51) ^†

Emphasis, \({\upgamma}_{05}\)

–

–

8.22 (3.53)^†

.51 (3.34) ^†

 Safe, \({\upgamma}_{06}\)

–

–

− 4.14 (3.02) ^†

1.36 (2.55) ^†

Ses slope, \({\upbeta }_{1}\)

 Intercept, \({\upgamma}_{10}\)

–

13.77 (.87)

–

10.46 (.86)

Engage slope, \({\upbeta }_{2}\)

 Intercept, \({\upgamma}_{20}\)

–

–

3.35 (.85)

3.06 (.82)

Litnum slope, \({\upbeta }_{3}\)

 Intercept, \({\upgamma}_{30}\)

–

–

7.62 (.68)

5.77 (.67)

Liking slope, \({\upbeta }_{4}\)

 Intercept, \({\upgamma}_{40}\)

–

–

13.37 (1.08)

12.35 (.96)

Preschool slope, \({\upbeta }_{5}\)

 Intercept, \({\upgamma}_{50}\)

–

–

18.80 (2.81)

14.27 (2.80)

Student level residual, \({r}_{ij}\)

5454.20

5081.27

4668.49

4482.05

Mean achievement, \({u}_{0j}\)

3530.90

1171.69

2141.26

982.54

ses slope, \({u}_{1j}\)

–

3.14

–

1.48

engage slope, \({u}_{2j}\)

–

–

0.85

1.59

litnum slope, \({u}_{3j}\)

–

–

0.62

0.33

liking slope, \({u}_{4j}\)

–

–

8.61

0.68

From model 1

 Level-1, \(\Delta \sigma ^{2}\)

–

.07

.14

.18

 Level-2, \(\Delta \tau _{{00}}\)

–

.67

.39

.72

From model 2

 Level-1, \(\Delta \sigma ^{2}\)

–

–

–

.12

 Level-2, \(\Delta \tau _{{00}}\)

–

–

–

.16

From model 3

 Level-1, \(\Delta \sigma ^{2}\)

–

–

–

.04

 Level-2, \(\Delta \tau _{{00}}\)

–

–

–

.54