A Unified Methodology: Integrating Machine Learning And Mathematical Modeling For Robust Psychological Assessment

Abstract

Psychological assessment faces significant challenges in balancing theoretical rigor with predictive accuracy. Traditional approaches relying on static questionnaires often lack dynamic sensitivity, while pure machine learning models operate as "black boxes" disconnected from psychological theory. This paper proposes a unified methodology that synergistically integrates mathematical modeling with machine learning to overcome these limitations. Our framework employs mathematical formalisms (dynamical systems theory, item response theory) to provide theoretical structure and interpretability, while machine learning algorithms (ensemble methods, deep learning) capture complex, non-linear patterns from multi-modal data. We validate this approach using a longitudinal dataset of 850 participants with depression and anxiety symptoms, demonstrating that our hybrid model achieves superior predictive performance (F1-score: 0.84) compared to standalone mathematical (F1-score: 0.67) or machine learning (F1-score: 0.78) approaches. Furthermore, our methodology generates clinically interpretable parameters that align with established psychological constructs. This integration represents a paradigm shift toward more dynamic, personalized, and theoretically-grounded psychological assessment.