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

Recommendations

Info

Appendix E: Technical details on multi-level modelling <strong>The</strong> general multi-level model fitted in this analysis can be written as where ~0, , and is the student level variance and and are the variance components for school intercepts and school slopes respectively, such that ~ 0 0 , , where represents the variability in school intercepts, is the variability in slopes and is the covariance between intercepts and slopes. In the mixed-model framework, this model is written as where the terms in [ ] represent fixed effects and those in ( ) represent random effects. <strong>The</strong> fixed effects are fitted and tested first and only random effects included are , and , that is, the random school and individual level variances. <strong>The</strong> final tests conducted are those that fit the random effects for the individual level characteristics ( ). Different strategies exist for adding student and school-level predictor variables to build a multi-level model (Hox 2010; Twisk 2006). In this study, random-intercept models were fitted for each outcome that contained all student and school-level predictors as fixed effects. Using Wald tests, nonsignificant predictors were successively eliminated from the models. Finally, statistically significant random coefficients for student-level predictors were included (using changes in log-likelihoods). <strong>The</strong> final model for each respective outcome contained all statistically significant fixed and random effects at the student level, as well as all statistically significant fixed effects at the school level. <strong>The</strong> interpretation <strong>of</strong> the coefficients resulting from a multi-level model is the same as for ordinary regression. However, given that <strong>schools</strong> are fitted as random effects the predicted means or probabilities for <strong>schools</strong> are based on Best Linear Unbiased Prediction (BLUP; Henderson 1975). Appropriate student- and school-level weights were applied to all multi-level analyses. Cases with missing data were excluded. Even though multiple imputation is the recommended approach for handling missing data (see Gemici, Bednarz & Lim 2011), s<strong>of</strong>tware for multiple imputation procedures in multi-level models (as outlined in Goldstein et al. 2009) is currently still in an experimental stage. <strong>The</strong>refore, it was decided to not use multiple imputation in the context <strong>of</strong> this multi-level modelling study. <strong>The</strong> intra-class correlation (ICC) captures the extent to which individuals within a school are similar to each other. In particular, the ICC provides a mechanism for determining how much <strong>of</strong> the total variation in a particular outcome can be attributed to each level included (that is, students, school) in the multi-level model. High values <strong>of</strong> the ICC indicate that <strong>schools</strong> play an important part in explaining the variation in the given outcome. Small values indicate that student background characteristics play a larger part in explaining the relationship with the outcome <strong>of</strong> interest. 48 <strong>The</strong> <strong>impact</strong> <strong>of</strong> <strong>schools</strong> on young people’s transition to university
In this paper, the ICC for the continuous TER outcome yields the percentage <strong>of</strong> total variation attributable to <strong>schools</strong> and individuals. For the binary university enrolment outcome, the error variance is constant at (Hedeker 2003) and the ICC does not provide the same information. For this model, the change in actual variance components is a more appropriate measure <strong>of</strong> variance explained (see appendix F, table F1). NCVER 49
Page 1: LONGITUDINAL SURVEYS OF AUSTRALIAN
Page 4 and 5: © Commonwealth of
Page 7 and 8: Contents Tables and figures 6 Execu
Page 9 and 10: 8 Cluster analysis of</stro
Page 11 and 12: can be identified statistically but
Page 13 and 14: Current knowledge about school effe
Page 15 and 16: Analysis Data and sample This study
Page 17 and 18: Academic orientation Academic orien
Page 19 and 20: Results This section first presents
Page 21 and 22: School attribute Categories ß SE J
Page 23 and 24: variance which can be attributed to
Page 25 and 26: School attribute Categories ß SE O
Page 27 and 28: student—teacher ratio, competitiv
Page 29 and 30: Figure 6 Caterpillar plots
Page 31 and 32: Comparing influential school attrib
Page 33 and 34: in over two-thirds of</stro
Page 35 and 36: Table 8 Geographic distribution <st
Page 37 and 38: Figure 10 Components of</st
Page 39 and 40: References Australian Curriculum, A
Page 41 and 42: Appendix A: Descriptive statistics
Page 43 and 44: School attribute Categories TER (N
Page 45 and 46: Perceptions of the
Page 47 and 48: Figure C1 Scree plot from SES facto
Page 49: Figure D1 Scree plot from perceptio
Page 53 and 54: Table F2 Results for student-level
Page 55 and 56: School attribute Categories df Join
Page 57 and 58: Table F5 Results for school-level p
Page 59: Appendix G: Information on the Logi

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

Create successful ePaper yourself

Delete template?

Save as template?