Background: Efficacy trials in education often possess a motivating theory of change: how and why should the desired improvement in outcomes occur as a consequence of the intervention? In scenarios with repeated measurements, certain subgroups may be more or less likely to manifest a treatment effect; the theory of change (TOC) provides guidance…

Multilevel modeling (MLM) is frequently used to detect cluster-level group differences in cluster randomized trial and observational studies. Group differences on the outcomes (posttest scores) are detected by controlling for the covariate (pretest scores) as a proxy variable for unobserved factors that predict future attributes. The pretest and…