Model 1

Model 2

Model 3

Fixed effects

Intercept

74.06 (1.61)*

75.7 (0.77)*

78.44 (2.10)*

Sex

1.17 (0.64)

1.08 (0.65)

1.13 (0.62)

Grade

1.86 (0.79)*

1.86 (0.81)*

5.71 (2.76)*

School

13.24 (2.56)*

School × grade

17.44 (3.45)*

Area

3.54 (0.66)*

Random effects

Intercept (school)

17.15 (9.69)*

Model fit

AIC

12768.4

12831.2

12575.9

BIC

12768.5

12836.6

12581.2