Controlling Homophily in Social Network Regression Analysis by Machine Learning

Across social science disciplines, empirical studies related to social networks have become the most popular research subjects in recent years. A frequently examined topic within these studies is the estimation of peer influence while controlling for homophily effects. However, although researchers may have access to all observable homophily variables, there is scarce literature addressing latent homophily effects stemming from unobservable features. Recent endeavors have demonstrated the efficacy of node embeddings derived from network structure in controlling latent homophily. Inspired by the network embedding research, this study introduces two methods that integrate node embeddings to better control latent homophily, particularly the nonlinear latent homophily effect. The first method uses double machine learning in the partially linear regression literature to alleviate estimation bias. The second method estimates peer influence effects directly by a novel neural network model. Our experimentation results show that our approaches outperform existing estimators in reducing the omitted variable bias due to homophily effects in network regression models. Theoretical analysis of two new estimation methods is also provided in this paper.