The impact of schools on young people's transition to university

Appendix F: Results from multilevel
modelling
Table F1 provides the variance components from the initial null model and the final model for each
outcome. <strong>The</strong> null model is the basic variance components model with a random intercept but
without any predictors. <strong>The</strong> final model is the model with all statistically significant student and
school-level predictors for each respective outcome. σ 2 school shows the unexplained variance in school
intercepts. σ 2 gender and σ 2 ses are variance components for the amount <strong>of</strong> variation explained by student
gender and student socioeconomic status in <strong>schools</strong> (that is, they represent variation at the individual
level). σ 2 e is the unexplained variation between students in <strong>schools</strong>. Note that for university
enrolment σ 2 gender and σ 2 ses were not statistically significant random effects.
Table F1 Variance components for null and final models across outcomes
TER
University
Var. comp. Null model Final model Null model Final model
σ 2 school 57.34 20.36 1.08 0.06
σ 2 gender 3.11
σ 2 ses 28.21
σ 2 e 233.05 143.56
Total 290.39 195.24 4.37 3.35
<strong>The</strong> variance component for <strong>schools</strong> (σ 2 school) has decreased substantially in the final models when
compared with the null models for each respective outcome. For the TER outcome, the reduction in
the variance component for <strong>schools</strong> (σ 2 school ) must be considered in conjunction with the reduction in
error variance (σ 2 e) because the multi-level model explains both school and student-level variance. As
the models include more predictor variables, the total variation present in TER is reduced. A logistic
model is used for the university enrolment outcomes, so the error variance remains constant at
(Hedeker 2003).
Tables F2—F7 provide detailed results from the multi-level modelling for TER and the probability <strong>of</strong>
university enrolment at age 19. <strong>The</strong> following applies to these tables:
All statistical tests were based on a significance level <strong>of</strong> α = 0.05.
All continuous predictors are grand-mean-centred.
<strong>The</strong> reference category for categorical predictors is marked as [R].
For categorical predictors, Wald χ 2 statistics indicate the joint value.
<strong>The</strong> final model shows only statistically significant predictors, so all Wald χ 2 values are bolded. For
categorical predictors, those categories that are statistically significantly different from the
reference category have bolded beta coefficients and standard errors.
50 <strong>The</strong> <strong>impact</strong> <strong>of</strong> <strong>schools</strong> on young people’s transition to university