Adaptive Centering with Random Effects: An Alternative to the Fixed Effects Model for Studying Time-Varying Treatments in School Settings

Fixed effects models are often useful in longitudinal studies when the goal is to assess the impact of teacher or school characteristics on student learning. In this article, I introduce an alternative procedure: adaptive centering with random effects. I show that this procedure can replicate the fixed effects analysis while offering several comparative advantages: the incorporation into standard errors of multiple levels of clustering; the modeling of heterogeneity of treatment effects; the estimation of effects of treatments at multiple levels; and computational simplicity. After illustrating these ideas in a simple setting, the article formulates a general linear model with adaptive centering and random effects and derives efficient estimates and standard errors. The results apply to studies that have an arbitrary number of nested and cross-classified factors such as time, students, classrooms, schools, districts, or states.