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.

The ability of school (or teacher) value-added models to provide unbiased estimates of school (or teacher) effects rests on a set of assumptions. In this article, we identify six assumptions that are required so that the estimands of such models are well defined and the models are able to recover the desired parameters from observable data. These assumptions are (1) manipulability, (2) no interference between units, (3) interval scale metric, (4) homogeneity of effects, (5) strongly ignorable assignment, and (6) functional form. We discuss the plausibility of these assumptions and the consequences of their violation. In particular, because the consequences of violations of the last three assumptions have not been assessed in prior literature, we conduct a set of simulation analyses to investigate the extent to which plausible violations of them alter inferences from value-added models. We find that modest violations of these assumptions degrade the quality of value-added estimates but that models that explicitly account for heterogeneity of school effects are less affected by violations of the other assumptions.