Estimating Causal Peer Influence in Homophilous Social Networks by Inferring Latent Locations

TL;DR

This paper demonstrates that in certain social network models, latent homophily can be estimated from network structure, enabling unbiased estimation of social influence effects in observational data.

Contribution

It introduces methods to consistently estimate latent attributes from network data, allowing for unbiased social influence analysis in models with latent homophily.

Findings

Latent homophily can be estimated from network patterns in stochastic block and latent space models.

Controlling for estimated attributes yields asymptotically unbiased social influence estimates.

Bias decreases at a rate proportional to the information content of the network about latent attributes.

Abstract

Social influence cannot be identified from purely observational data on social networks, because such influence is generically confounded with latent homophily, i.e., with a node's network partners being informative about the node's attributes and therefore its behavior. If the network grows according to either a latent community (stochastic block) model, or a continuous latent space model, then latent homophilous attributes can be consistently estimated from the global pattern of social ties. We show that, for common versions of those two network models, these estimates are so informative that controlling for estimated attributes allows for asymptotically unbiased and consistent estimation of social-influence effects in linear models. In particular, the bias shrinks at a rate which directly reflects how much information the network provides about the latent attributes. These are the first results on the consistent non-experimental estimation of social-influence effects in the presence of latent homophily, and we discuss the prospects for generalizing them.