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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.