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.

翻译：本研究探讨同伴榜样对药物滥用和犯罪行为治疗社区（TCs）中成功毕业的影响。我们利用三个TCs的数据，这些数据记录了居民间肯定性交流的交换记录及其精确的入出院日期，使我们能够构建同伴网络并定义感兴趣的因果效应。榜样效应衡量了当一位居民（自我）能够在自身出院前观察到其同伴之一毕业与未毕业时，其预期结果的差异。为了在观测数据存在未观测同质性的情况下识别同伴影响，我们采用潜变量模型对网络进行建模。我们证明，当从未观测网络中估计未观测潜位置时，我们的同伴影响估计量具有渐近无偏性。此外，我们提出了一种测量误差偏误校正方法，以进一步减少因估计潜位置而产生的偏误。模拟结果表明，所提出的潜在同质性调整和偏误校正在有限样本中表现良好。我们还将该方法扩展到使用probit模型的二值响应情况。我们的研究结果表明，同伴毕业对居民毕业具有积极影响，且该影响因性别、种族及榜样效应的定义而异。一项反事实分析量化了干预措施对直接接受治疗的居民及其通过网络传播间接影响的同伴的潜在益处。