A Hybrid Mathematical Framework Combining Logistic Regression and Neural Networks with Explainable AI Techniques for Mental Health Prediction

Abstract

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.