Causal Inference with Multilevel Models: The Electric Company Example

Estimating causal effects from clustered or grouped data requires careful attention to the hierarchical structure of observations. When units are nested within groups such as students within classrooms, or patients within hospitals—ignoring this structure can lead to incorrect standard errors, inefficient estimates, and invalid causal inferences. Multilevel models provide a principled framework for handling such data while leveraging the advantages of partial pooling across groups.

This notebook reproduces and extends the analysis from Chapter 23 of Gelman and Hill’s “Data Analysis Using Regression and Multilevel/Hierarchical Models”. We demonstrate two complementary approaches to modeling treatment effects in hierarchical data: first, a model with varying intercepts that efficiently controls for group-level confounding, and second, a more flexible covariance model that allows treatment effects themselves to vary across groups. Together, these models illustrate how multilevel structures enhance both the efficiency and interpretability of causal effect estimation. In addition to reproducing the analysis, we show how to efficiently vectorize the model (across grades and pairs) using PyMC.