Asymptotic failure of peer effects in network regression models

Asymptotic failure of peer effects in network regression models

Abstract

Network autoregressive models seek to model peer effects such as contagion and interference, in which node-level responses or covariates may influence one another. These models are frequently deployed by practitioners in sociology and econometrics, typically in the form of linear-in-means models, in which local averages of node-level covariates and responses are used as predictors. In highly structured networks, previous work has shown that peer effects in linear-in-means models are collinear with other regression terms, and thus cannot be estimated, but this collinearity is widely believed to be ignorable, as peer effects are typically identified in empirical networks. In this work, we show a concerning negative result: under linear-in-means models, when node-level covariates are independent of network structure, peer effects become increasingly collinear with other regression terms as the network size (i.e., number of nodes) grows, and are inestimable asymptotically. We also show a narrow positive result: under certain latent space network models, some peer effects remain identified as the network size grows, albeit under rather stringent conditions. Our results suggest that linear models for peer effects are appropriate in far fewer settings than was previously believed.

Bio

Keith Levin is an assistant professor in the Department of Statistics at University of Wisconsin-Madison. He completed his Ph.D. in Computer Science at Johns Hopkins University. Prior to joining Wisconsin, he was a postdoctoral fellow in the Department of Statistics at University of Michigan. His research interests include statistical network analysis, concentration inequalities, clustering and subspace estimation.