Estimating network-mediated causal effects via spectral embeddings

The last several years have seen a renewed and concerted effort to incorporate network data into standard tools for regression analysis, and to make network-linked data legible to working scientists. Thus far, this literature has primarily developed tools to infer associative relationships between nodal covariates and network structure. In this work, we augment a statistical model for network regression with counterfactual assumptions. Under this model, causal effects can be partitioned into a direct effect uninfluenced by the network, and an indirect effect that is induced by homophily. The method is a conceptually straightforward integration of latent variable models for networks into the well-known product-of-coefficients mediation estimator. Our method is semi-parametric, easy to implement, and highly scalable.