# Causal inference, social networks, and chain graphs

## TL;DR

This paper introduces a simplified chain graph model for causal inference in social networks, addressing data complexity and high dimensionality issues, and demonstrates its application to Supreme Court decision data.

## Contribution

It proposes a parsimonious chain graph framework for causal inference in network settings with interference and contagion, improving practicality and interpretability.

## Key findings

- Chain graph models approximate the distribution of network data with interference.
- Application to Supreme Court data reveals insights into collective decision-making.
- Simulation studies support the model's effectiveness in causal inference.

## Abstract

Traditionally, statistical and causal inference on human subjects rely on the assumption that individuals are independently affected by treatments or exposures. However, recently there has been increasing interest in settings, such as social networks, where individuals may interact with one another such that treatments may spill over from the treated individual to their social contacts and outcomes may be contagious. Existing models proposed for causal inference using observational data from networks of interacting individuals have two major shortcomings. First, they often require a level of granularity in the data that is practically infeasible to collect in most settings, and second, the models are high-dimensional and often too big to fit to the available data. In this paper we illustrate and justify a parsimonious parameterization for network data with interference and contagion. Our parameterization corresponds to a particular family of graphical models known as chain graphs. We argue that, in some settings, chain graph models approximate the marginal distribution of a snapshot of a longitudinal data generating process on interacting units. We illustrate the use of chain graphs for causal inference about collective decision making in social networks using data from U.S. Supreme Court decisions between 1994 and 2004 and in simulations.