An Approach to Causal Inference over Stochastic Networks

TL;DR

This paper introduces a Bayesian causal inference framework for stochastic networks with unobserved structures and evolving covariates, addressing complex dependencies and spillover effects in social network analysis.

Contribution

It develops a joint ERNM-based model for causality in unobserved, stochastic networks with dynamic covariates, avoiding restrictive assumptions and enabling Bayesian inference.

Findings

Simulation study confirms validity of the approach.

Framework effectively captures causal effects in complex networks.

Case study demonstrates practical applicability in social settings.

Abstract

Claiming causal inferences in network settings necessitates careful consideration of the often complex dependency between outcomes for actors. Of particular importance are treatment spillover or outcome interference effects. We consider causal inference when the actors are connected via an underlying network structure. Our key contribution is a model for causality when the underlying network is unobserved and the actor covariates evolve stochastically over time. We develop a joint model for the relational and covariate generating process that avoids restrictive separability assumptions and deterministic network assumptions that do not hold in the majority of social network settings of interest. Our framework utilizes the highly general class of Exponential-family Random Network models (ERNM) of which Markov Random Fields (MRF) and Exponential-family Random Graph models (ERGM) are special cases. We present potential outcome based inference within a Bayesian framework, and propose a simple modification to the exchange algorithm to allow for sampling from ERNM posteriors. We present results of a simulation study demonstrating the validity of the approach. Finally, we demonstrate the value of the framework in a case-study of smoking over time in the context of adolescent friendship networks.