Hierarchical Causal Models

TL;DR

This paper introduces hierarchical causal models to analyze cause-and-effect relationships in nested data structures, extending existing causal frameworks with new identification techniques and estimation methods, demonstrated through simulations and a classic study.

Contribution

It extends structural causal models with hierarchical structures, providing new identification techniques and estimation methods for nested data.

Findings

Hierarchical data can enable causal identification not possible with non-hierarchical summaries.

The proposed methods work effectively in simulations and real data reanalysis.

Hierarchical Bayesian models are useful for estimating causal effects in nested data.

Abstract

Scientists often want to learn about cause and effect from hierarchical data, collected from subunits nested inside units. Consider students in schools, cells in patients, or cities in states. In such settings, unit-level variables (e.g. each school's budget) may affect subunit-level variables (e.g. the test scores of each student in each school) and vice versa. To address causal questions with hierarchical data, we propose hierarchical causal models, which extend structural causal models and causal graphical models by adding inner plates. We develop a general graphical identification technique for hierarchical causal models that extends do-calculus. We find many situations in which hierarchical data can enable causal identification even when it would be impossible with non-hierarchical data, that is, if we had only unit-level summaries of subunit-level variables (e.g. the school's average test score, rather than each student's score). We develop estimation techniques for hierarchical causal models, using methods including hierarchical Bayesian models. We illustrate our results in simulation and via a reanalysis of the classic "eight schools" study.