Applying the hierarchical linear model to longitudinal data

Educational researchers and school administrators frequently evaluate academic outcomes collected from cross-sectional sampling designs with overt nested structures, such as when students are nested within schools. More recently, interest has focused on the longitudinal collection of academic outcomes to evaluate a student's growth across time. In a longitudinal context, the repeatedly measured academic outcomes are nested within a student. Proper analysis of longitudinal data requires the hierarchical linear model to quantify the extra correlations within students created by the nested sampling structure. In this article, we introduce the hierarchical linear model used to quantify and predict between-student differences in a repeatedly measured continuous maths achievement outcome. This introduction is presented as a conversation representative of those we have frequently with individuals who lack statistical training in hierarchical linear models for longitudinal data. Specifically, we cover why repeated-measures ANOVA may not always be appropriate, how the hierarchical linear model can be used to quantify between-student differences in change and how student- and occasion-level predictors can be properly modelled and interpreted.