Marginal Mean Weighting Through Stratification: Adjustment for Selection Bias in Multilevel Data

Abstract

Defining causal effects as comparisons between marginal population means, this article introduces marginal mean weighting through stratification (MMW-S) to adjust for selection bias in multilevel educational data. The article formally shows the inherent connections among the MMW-S method, propensity score stratification, and inverse-probability-of-treatment weighting (IPTW). Both MMW-S and IPTW are suitable for evaluating multiple concurrent treatments, and hence have broader applications than matching, stratification, or covariance adjustment for the propensity score. Furthermore, mathematical consideration and a series of simulations reveal that the MMW-S method has incorporated some important strengths of the propensity score stratification method, which generally enhance the robustness of MMW-S estimates in comparison with IPTW estimates. To illustrate, the author applies the MMW-S method to evaluations of within-class homogeneous grouping in early elementary reading instruction.