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.