Graph Neural Networks for Generalized Mundlak Estimator under Network Confounding

This paper proposes a generalized Mundlak estimator based on graph neural networks (GME-GNN). The estimator is designed to mitigate bias arising from group-level heterogeneity and to accommodate within-group dependence among individuals. Traditional fixed-effects models handle group heterogeneity via group-specific intercepts, but require overly strict linear additivity and intra-group independence assumptions, and are confined to within-group comparisons. Rather than relying on intercepts, GME-GNN uses aggregated group-level balancing statistics to fully control between-group confounding, enabling valid cross-group comparisons and relaxing linearity constraints. It further employs graph neural network message-passing to adaptively learn nonlinear representations and capture intra-group interaction effects. Theoretical analysis shows that the estimator satisfies double robustness and is asymptotically normal. Simulation and empirical studies confirm its performance.