Multilevel Propensity Score Methods for Estimating Causal Effects: A Latent Class Modeling Strategy

Abstract

Despite their appeal, randomized experiments cannot always be conducted, for example, due to ethical or practical reasons. In order to remove selection bias and draw causal inferences from observational data, propensity score matching techniques have gained increased popularity during the past three decades. Although propensity score methods have been studied extensively for single-level data, the additional assumptions and necessary modifications for applications with multilevel data are understudied. This is troublesome considering the abundance of nested structures and multilevel data in the social sciences. This study summarizes issues and challenges for causal inference with observational multilevel data in comparison with single-level data, and discusses strategies for multilevel matching methods. We investigate within- and across-cluster matching strategies and emphasize the importance of examining both overlap within clusters and potential heterogeneity in the data before pooling cases across clusters. We introduce a multilevel latent class logit model approach that encompasses the strengths of within- and across-matching techniques. Simulation results support the effectiveness of our method in estimating treatment effects with multilevel data even when selection processes vary across clusters and a lack of overlap exists within clusters.