UNCOVERING LATENT STRESS DIMENSIONS IN UNIVERSITY STUDENTS: A PCA SIMULATION STUDY WITH SENSITIVITY ANALYSIS AND THE DYNAMIC STRESS SIGNATURE FRAMEWORK

Abstract

Academic stress and burnout in university students manifest through multiple interrelated behavioral, cognitive, and physiological channels whose co-variation structure is routinely discarded by conventional statistical analysis. This simulation study applies principal component analysis (PCA) to a synthetic eight-variable behavioral dataset generated from a three-factor latent structure representing academic burnout — Academic Pressure, Psychological Depletion, and Performance Dread — and demonstrates that PCA recovers this structure with high fidelity while delivering measurable predictive advantages over raw-variable regression. The base scenario (n = 237) recovers the three-component structure explaining 86.8% of total variance, reduces mean variance inflation factor from 4.1 to 1.0, and achieves an AIC improvement of 21.6 units over conventional regression. A systematic sensitivity analysis across eight sample sizes (n = 40 to 400) and seven inter-variable correlation levels shows that Tucker's congruence coefficient reaches φ ≥ 0.95 reliably at n ≥ 200, and that PCA's AIC advantage persists across all correlation conditions tested (ΔAIC = 14.7 to 17.1). At very small samples (n = 40), component recovery degrades substantially (mean φ = 0.87, stable solutions in only 36% of replications), establishing a practical lower bound on the method's applicability. Beyond the cross-sectional findings, this paper introduces the dynamic stress signature: each student's characteristic temporal sequence of dominant components across the academic calendar, individually unique and recoverable by longitudinal PCA, analogous to a stress fingerprint. The simulation design, sensitivity boundaries, and longitudinal framework together constitute a complete methodological guide for applied burnout researchers intending to deploy PCA in behavioral datasets.

Keywords: principal component analysis, simulation study, academic burnout, dynamic stress signature, sensitivity analysis, Tucker congruence, parallel analysis, Varimax rotation, multicollinearity, longitudinal PCA