(untitled) (Contemporary Mathematics, 2025)
Accurate prediction of mental health outcomes is vital for early intervention and effective resource allocation, yet existing methods often struggle to balance predictive accuracy with interpretability, a key requirement in clinical and policy settings. This study addresses this dual challenge by introducing a hybrid mathematical framework that combines Multiple Logistic Regression (MLR), known for its transparency, is used with a Multilayer Perceptron (MLP), which is recognized for its ability to capture complex non-linear patterns. Explainability is further enhanced through the incorporation of SHapley Additive exPlanations (SHAP) for global feature attribution and Local Interpretable Model-Agnostic Explanations (LIME) for case-specific interpretive clarity. Applied to a structured dataset of 310 university students, the proposed hybrid model achieved a prediction accuracy of 97.81% and sensitivity of 94.74%, significantly outperforming the standalone MLR model (80.65% accuracy). This performance gain is not only statistically validated but also accompanied by transparent, interpretable insights into the contribution of sociodemographic factors to mental health outcomes. The proposed framework offers a practical solution to the long-standing trade-off between model accuracy and explainability, and has the potential to be applied across various healthcare domains where interpretability is as crucial as predictive performance.