From Friendship Networks to Classroom Dynamics: Leveraging Neural Networks, Instrumental Variable and Genetic Algorithms for Optimal Educational Outcomes

This study uses data from the China Educational Panel Survey (CEPS) to design a classroom assignment policy that maximizes peer effects. Our approach comprises three steps: firstly, we develop a friendship formation discrete choice model and estimate it with an interpretable neural network architecture, PeerNN, generating an adjacency-probability matrix $\Omega$ that reflects friendship formation probabilities. Secondly, we incorporate $\Omega$ into a linear-in-means model to estimate peer effects. The peer effect parameter, $\beta$, has a different interpretation from the conventional linear-in-means model and opens up a strategic scope of mean-maximizing classroom assignment policy. By exploiting the conditional random classroom assignment in many Chinese middle schools, we construct a valid instrument to address the endogeneity issue induced by $\Omega$ and consistently estimate $\beta$. Lastly, utilizing the estimates of $\Omega$ and $\beta$, we employ a genetic algorithm (GA) to search for the mean-maximizing class assignment policy. Though the result is much more efficient (i.e. more positive average peer effect) than random classroom assignment (i.e. the current practice in most Chinese middle schools), GA policy is highly inequitable: a small number of students are predicted to experience severely negative peer effects. To balance students' academic performance with educational equity, we propose a fairness metric and penalize classroom assignment that generates large variances in peer effects. The modified method is called algorithmically fair genetic algorithm (AFGA). AFGA policy is less efficient but much more equitable. We allow user-defined parameters for AFGA such that the school principals can adjust the trade-off between efficiency and equity according to their preferences.