A Mathematical Framework for Temporal Modeling and Counterfactual Policy Simulation of Student Dropout

This study proposes a temporal modeling framework with a counterfactual policy-simulation layer for student dropout in higher education, using LMS engagement data and administrative withdrawal records. Dropout is operationalized as a time-to-event outcome at the enrollment level; weekly risk is modeled in discrete time via penalized, class-balanced logistic regression over person--period rows. Under a late-event temporal holdout, the model attains row-level AUCs of 0.8350 (train) and 0.8405 (test), with aggregate calibration acceptable but sparsely supported in the highest-risk bins. Ablation analyses indicate performance is sensitive to feature set composition, underscoring the role of temporal engagement signals. A scenario-indexed policy layer produces survival contrasts $ΔS(T)$ under an explicit trigger/schedule contract: positive contrasts are confined to the shock branch ($T_{\rm policy}=18$: 0.0102, 0.0260, 0.0819), while the mechanism-aware branch is negative ($ΔS_{\rm mech}(18)=-0.0078$, $ΔS_{\rm mech}(38)=-0.0134$). A subgroup analysis by gender quantifies scenario-induced survival gaps via bootstrap; contrasts are directionally stable but small. Results are not causally identified; they demonstrate the framework's capacity for internal structural scenario comparison under observational data constraints.

Temporal Dropout Risk in Learning Analytics: A Harmonized Survival Benchmark Across Dynamic and Early-Window Representations

Student dropout is a persistent concern in Learning Analytics, yet comparative studies frequently evaluate predictive models under heterogeneous protocols, prioritizing discrimination over temporal interpretability and calibration. This study introduces a survival-oriented benchmark for temporal dropout risk modelling using the Open University Learning Analytics Dataset (OULAD). Two harmonized arms are compared: a dynamic weekly arm, with models in person-period representation, and a comparable continuous-time arm, with an expanded roster of families -- tree-based survival, parametric, and neural models. The evaluation protocol integrates four analytical layers: predictive performance, ablation, explainability, and calibration. Results are reported within each arm separately, as a single cross-arm ranking is not methodologically warranted. Within the comparable arm, Random Survival Forest leads in discrimination and horizon-specific Brier scores; within the dynamic arm, Poisson Piecewise-Exponential leads narrowly on integrated Brier score within a tight five-family cluster. No-refit bootstrap sampling variability qualifies these positions as directional signals rather than absolute superiority. Ablation and explainability analyses converged, across all families, on a shared finding: the dominant predictive signal was not primarily demographic or structural, but temporal and behavioral. Calibration corroborated this pattern in the better-discriminating models, with the exception of XGBoost AFT, which exhibited systematic bias. These results support the value of a harmonized, multi-dimensional benchmark in Learning Analytics and situate dropout risk as a temporal-behavioral process rather than a function of static background attributes.