Enhancing Educational Outcome with Machine Learning: Modeling Friendship Formation, Measuring Peer Effect and Optimizing Class Assignment

In this paper, we look at a school principal's class assignment problem. We break the problem into three stages (1) friendship prediction (2) peer effect estimation (3) class assignment optimization. We build a micro-founded model for friendship formation and approximate the model as a neural network. Leveraging on the predicted friendship probability adjacent matrix, we improve the traditional linear-in-means model and estimate peer effect. We propose a new instrument to address the friendship selection endogeneity. The estimated peer effect is slightly larger than the linear-in-means model estimate. Using the friendship prediction and peer effect estimation results, we simulate counterfactual peer effects for all students. We find that dividing students into gendered classrooms increases average peer effect by 0.02 point on a scale of 5. We also find that extreme mixing class assignment method improves bottom quartile students' peer effect by 0.08 point.