B0723
Title: Estimating network-mediated causal effects via spectral embeddings
Authors: Keith Levin - University of Wisconsin (United States) [presenting]
Alex Hayes - University of Wisconsin-Madsion (United States)
Abstract: Causal inference for observational network data is an area of active interest owing to the ubiquity of network data in the social sciences. Unfortunately, the complicated dependency structure of network data presents an obstacle to many popular causal inference procedures. The task of mediation analysis for network data is considered. A model in which mediation occurs in a latent node embedding space is presented. Under this model, node-level interventions have causal effects on nodal outcomes, and these effects can be partitioned into a direct effect independent of the network and an indirect effect induced by homophily. To estimate these network-mediated effects, nodes are embedded into a low-dimensional Euclidean space. These embeddings are then used to fit two ordinary least squares models: (1) an outcome model that characterizes how nodal outcomes vary with nodal treatment, controls, and position in latent space, and (2) a mediator model that characterizes how latent positions vary with nodal treatment and controls. It is proven that the estimated coefficients are asymptotically normal about the true coefficients under a sub-gamma generalization of the random dot product graph, a widely-used latent space model. Further, it is shown that these coefficients can be used in product-of-coefficients estimators for causal inference.
