# Hierarchical Causal Models

arXiv: https://arxiv.org/abs/2401.05330 · HTML: https://mlsanity.com/paper/2401.05330/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2024.

## Built on by (most cited first, 9 of 9)

- [EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments](https://mlsanity.com/paper/2607.05155/) (2026)
- [Differentiable Causal Discovery For Latent Hierarchical Causal Models](https://mlsanity.com/paper/2411.19556/) (2024)
- [Bayesian Hierarchical Invariant Prediction](https://mlsanity.com/paper/2505.11211/) (2025)
- [CLAM: Causal Spatial Disaggregation to Infer Local Effects From Coarse Data](https://mlsanity.com/paper/2608.08064/) (2026)
- [Compositional Models for Estimating Causal Effects](https://mlsanity.com/paper/2406.17714/) (2024)
- [Causal identification with Y0](https://mlsanity.com/paper/2508.03167/) (2025)
- [Relational Structural Causal Models](https://mlsanity.com/paper/2606.14892/) (2026)
- [Analysis of Public Schools Educational Performance Based on Causal Models and Hierarchical Clustering](https://mlsanity.com/paper/2607.14124/) (2026)
- [Causal Effect Identifiability in Causal Abstractions: A Strict Hierarchy of Criteria](https://mlsanity.com/paper/2610.13520/) (2026)

## Abstract (arXiv)

Causal questions often arise in settings where data are hierarchical: subunits are nested within units. Consider students in schools, cells in patients, or cities in states. In these settings, unit-level variables (e.g., a school's budget) may affect subunit-level outcomes (e.g., student test scores), and subunit-level characteristics may aggregate to influence unit-level outcomes. In this paper, we show how to analyze hierarchical data for causal inference. We introduce hierarchical causal models, which extend structural causal models and graphical models by incorporating inner plates to represent nested data structures. We develop a graphical identification technique for these models that generalizes do-calculus. We show that hierarchical data can enable causal identification even when it would be impossible with non-hierarchical data--for example, when only unit-level summaries are available. We develop estimation strategies, including using hierarchical Bayesian models. We illustrate our results in simulation and through a reanalysis of the classic "eight schools" study.