Causal Inference in Multilevel Settings in Which Selection Processes Vary Across Schools

In this report we focus on the use of propensity score methodology in multisite studies of the effects of educational programs and practices in which both treatment and control conditions are enacted within each of the schools in a sample, and the assignment to treatment is not random. A key challenge in applying propensity score methodology in such settings is that the process by which students wind up in treatment or control conditions may differ substantially from school to school. To help capture differences in selection processes across schools, and achieve balance on key covariates between treatment and control students in each school, we propose the use of multilevel logistic regression models for propensity score estimation in which intercepts and slopes are treated as varying across schools. Through analyses of the data from the Early Academic Outreach Program (EAOP), we compare the performance of this approach with other possible strategies for estimating propensity scores (e.g., single-level logistic regression models; multilevel logistic regression models with intercepts treated as random and slopes treated as fixed). Furthermore, we draw attention to how the failure to achieve balance within each school can result in misleading inferences concerning the extent to which the effect of a treatment varies across schools, and concerning factors (e.g., differences in implementation across schools) that might dampen or magnify the effects of a treatment.