Network Influence with Latent Homophily and Measurement Error

Modeling social influence on outcomes of network-connected individuals is a central research question in several scientific disciplines. However, network influence cannot be identified from observational data because it is confounded with unobserved homophily. We propose a latent homophily-adjusted Spatial Autoregressive model (SAR) for networked responses to identify the causal contagion effects. The latent homophily is estimated from the spectral embedding of the network's adjacency matrix. We further develop maximum likelihood estimators for the parameters of the SAR model when covariates are measured with error. The bias-corrected MLE enjoys statistical consistency and asymptotic normality properties. We combine the estimated latent homophily with the bias corrected MLE in the SAR model to estimate network influence. Our simulations show that the methods perform well in finite samples. Applying our methodology to a data-set of female criminal offenders in a therapeutic community (TC), we provide causal estimates of network influence on graduation from the TC.