  We investigate peer role model influence on successful graduation from
Therapeutic Communities (TCs) for substance abuse and criminal behavior. We use
data from 3 TCs that kept records of exchanges of affirmations among residents
and their precise entry and exit dates, allowing us to form peer networks and
define a causal effect of interest. The role model effect measures the
difference in the expected outcome of a resident (ego) who can observe one of
their peers graduate before the ego's exit vs not graduating. To identify peer
influence in the presence of unobserved homophily in observational data, we
model the network with a latent variable model. We show that our peer influence
estimator is asymptotically unbiased when the unobserved latent positions are
estimated from the observed network. We additionally propose a measurement
error bias correction method to further reduce bias due to estimating latent
positions. Our simulations show the proposed latent homophily adjustment and
bias correction perform well in finite samples. We also extend the methodology
to the case of binary response with a probit model. Our results indicate a
positive effect of peers' graduation on residents' graduation and that it
differs based on gender, race, and the definition of the role model effect. A
counterfactual exercise quantifies the potential benefits of an intervention
directly on the treated resident and indirectly on their peers through network
propagation.
