# Identifying Peer Influence in Therapeutic Communities Adjusting for Latent Homophily

arXiv: https://arxiv.org/abs/2203.14223 · HTML: https://mlsanity.com/paper/2203.14223/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 87 references that are in the map.
- First posted on arXiv 27 Mar 2022.

## Builds on (most cited first, 12 of 12)

- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [A statistical interpretation of spectral embedding: the generalised random dot product graph](https://mlsanity.com/paper/1709.05506/) (2017)
- [Network cross-validation by edge sampling](https://mlsanity.com/paper/1612.04717/) (2016)
- [Limit theorems for eigenvectors of the normalized Laplacian for random graphs](https://mlsanity.com/paper/1607.08601/) (2016)
- [Community detection in multi-relational data with restricted multi-layer stochastic blockmodel](https://mlsanity.com/paper/1506.02699/) (2015)
- [Estimating Causal Peer Influence in Homophilous Social Networks by Inferring Latent Locations](https://mlsanity.com/paper/1607.06565/) (2016)
- [Additive and multiplicative effects network models](https://mlsanity.com/paper/1807.08038/) (2018)
- [Efficient Estimation for Random Dot Product Graphs via a One-step Procedure](https://mlsanity.com/paper/1910.04333/) (2019)
- [Estimating Social Influence from Observational Data](https://mlsanity.com/paper/2204.01633/) (2022)
- [Randomization Inference for Peer Effects](https://mlsanity.com/paper/1807.01635/) (2018)
- [Randomization tests for peer effects in group formation experiments](https://mlsanity.com/paper/1904.02308/) (2019)

## Built on by (most cited first, 1 of 1)

- [Spectral clustering for dependent community Hawkes process models of temporal networks](https://mlsanity.com/paper/2505.21845/) (2025)

## Abstract (arXiv)

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.