Student Mobility, Dosage, and Principal Stratification in School-Based RCTs

In school-based randomized control trials (RCTs), a common design is to follow student cohorts over time. For such designs, education researchers usually focus on the place-based (PB) impact parameter, which is estimated using data collected on all students enrolled in the study schools at each data collection point. A potential problem with this approach, however, is that the PB impact parameter could confound intervention effects on student mobility with more policy-relevant intervention effects on student achievement. Furthermore, the PB parameter pertains to students with different levels of intervention exposure, which complicates the interpretation of the impact findings. To address these issues, this article uses a principal stratification approach to examine the survivor average causal effect (SACE) parameter for original cohort students who would remain in their baseline study schools in either the treatment or control condition. The SACE parameter pertains to those who would receive maximum exposure to the intervention, and thus is a relevant parameter for dosage analyses. A strategy to estimate the SACE parameter is discussed using maximum likelihood (ML) methods for finite mixture models, the expectation-maximization (EM) algorithm, and robust standard errors to adjust for clustering. The estimation approach is demonstrated using data from a recent large-scale, school-based RCT where student mobility was common during the 3-year follow-up period.