Graph Neural Item Response Model for Networked Learning Environments

Learning increasingly occurs in socially and behaviorally connected environments, yet classical item response theory models treat examinees as independent and estimate latent abilities as free parameters. We introduce a graph neural item response model (GN-IRT) that integrates graph-regularized likelihood with neural representation learning for proficiency estimation in networked settings. GN-IRT preserves the standard two-parameter logistic (2PL) measurement structure while incorporating an observed learner interaction network through a graph-Laplacian penalty and modeling latent abilities as flexible nonlinear functions of learner covariates and network context. Network information regularizes the latent trait without altering the item response function or conditional independence given ability; multilevel and spatial IRT arise as special cases under appropriate adjacency specifications. We analyze the associated penalized latent-trait estimator, establishing existence, uniqueness, asymptotic consistency, preservation of first-order efficiency relative to classical 2PL, and Lipschitz stability under moderate network misspecification. We then show that the neural implementation inherits these first-order properties when approximation and optimization errors are asymptotically negligible. Simulations demonstrate improved ability recovery and predictive performance under joint covariate and network dependence, while preserving classical behavior under independence. An empirical application illustrates interpretable patterns of proficiency alignment in connected learning environments.