Hierarchical Linear Modeling: Guide and Applications

A multi-level analysis using NAEP data : examining the relationships among mathematics coaches and specialists, student achievement, and disability status.

“…Due to model complexity restrictions and in an effort for parsimony, only the slope of disability status (the level-1 variable of interest in this study) and the intercept were permitted to randomly vary between schools. The level-1 model provided the needed information to determine the within-school and between-school proportion reduction in variance, or the proportion of variance explained at level-1(within-school) and the proportion of variance explained at level-2 (between-school) by the addition of the student-level variables (Garson, 2013;Raudenbush & Bryk, 2002). …”

“…Continuous variables were centered around the grand mean (CGM) in HLM, as CGM allows for easy interpretability and may reduce multicollinearity (Garson, 2013). In order to have a consistent model across all content areas and research questions, variables remained in the model regardless of their significance levels.…”

“…With the addition of the set of contextual variables, the between-school proportion reduction of variance, or the proportion of variance explained at level-2 (between schools) was then determined by comparing the random coefficient model between-school variance to the contextual model between-school variance (Garson, 2013;Raudenbush & Bryk, 2002). Lastly, the inclusion of the treatment variable (i.e., MCS) in the final contextual model allowed the proportion of variance explained by the treatment variables above and beyond the control variables to be determined.…”

“…Full maximum likelihood was chosen as the type of estimation (over restricted maximum likelihood) for its consistent and efficient estimates, particularly with large sample sizes (Raudenbush & Bryk, 2002), as well as its recommendation for use with datasets containing missing values, given we did not conduct multiple imputation on the outcomes or predictors of interest (Garson, 2013).…”

“…The first analysis was a One-Way Random Effects ANOVA, often times called an unconditional or null model, which used the five plausible values for mathematics achievement as the outcome variables and included no predictor variables at level-1 or level-2. The unconditional model was used to calculate the intraclass correlation (ICC), which allows us to determine the need for a mixed model (Garson, 2013;McCoach & Adelson, 2010) by providing an indication of the magnitude of the cluster effect (Hox, 2002). Specifically, the ICC was used to determine the amount of variance in the level-1 mathematics scores (level-1 dependent variables) attributed to the clustering (school).…”