Causal Inference over Stochastic Networks

This is the software and data used for the paper:

Causal Inference over Stochastic Networks, by Duncan A. Clark and Mark S. Handcock, the Journal of the Royal Statistical Society, Series A, Jan 2024.

Summary

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 endogenous; where the ties between actors and the actor covariates are statistically dependent. We develop a joint model for the relational and covariate generating process that avoids restrictive separability and fixed network assumptions, as these rarely hold in realistic social settings. While our framework can be used with general models, we develop the highly expressive 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 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 in the context of adolescent friendship networks.

Keywords: Causality, Social Networks, Network models, Spillover, Contagion, Interference, Gibbs measures

Contents

fitting

This contains the main code for fitting real data, the simulation study and assessing the goodness-of-fit. The main files are listed below.

Add_health_fitting.R

Start with

fitting/Add_health_fitting.R

First, read ernm_notes for isses with the modified and extended version of the ernm package and other useful information.

GOF.R

This script carries out the triad census and makes the GOF plots contained in the paper

ernm_MPLE.R

This script does ERNM Pseudo likelihood estimation

sim_study.R

This script is the basis for the reproducible example of the sim study for the paper. For fuller sim study see sim_study_5.R

data

This contains the various data sources

functions

This contains the R functions called by the fitting functions.

fire.R

This is the Bayesian ERNM model fitting code

util.R

These are utility functions called by other functions

results

This contains R objects containing the actual results of the fits in the paper. There are mainly here to allow you to check that the code you have run is running correctly.