Measurement error and network homophily in autoregressive models of peer effects

Oregon Convention Center 

The autoregressive models of peer effects include the SAR model in cross sectional studies used to estimate the peer influence and the effects of covariates taking network dependence into account, and the longitudinal model to causally identify the effect of peer actions in the preceding time period. We investigate issues of measurement error and network homophily in both of these setups.
First, we investigate causal peer role model effect on successful graduation from Therapeutic Communities (TCs) for substance abuse using records of exchanges among residents and their entry and exit dates which allowed us to form peer networks and define a causal estimand. To identify peer influence in the presence of unobserved homophily, we model the network with a latent variable model and show that our peer influence estimator is asymptotically unbiased. Second, in the context of SAR model, while the model can be estimated with a QMLE approach, the detrimental effect of covariate measurement error on the QMLE and how to remedy it is currently unknown. We develop a measurement error-corrected ML estimator and show that it possesses statistical consistency and asymptotic normality properties.