Nonlinear associations between physical activity, sleep quality, and psychological distress in university students: a cross-sectional interpretable machine learning study

Background Physical activity and sleep disturbance may have nonlinear, interrelated associations with psychological distress. Objective: To develop an internally validated prediction model and explore MVPA–distress nonlinearity and statistical interaction with sleep disturbance. Methods A cross-sectional survey included 1,980 undergraduates from 68 classes at one university in Jiangsu Province, China. High-risk distress was defined as K10 ≥ 22. Development and internal testing used 48 classes ( n = 1,386) and 20 held-out classes ( n = 594), respectively; tuning used 10-fold GroupKFold. XGBoost was compared with logistic regression, support vector machine, and random forest. Test performance uncertainty was estimated using 2,000 class-level bootstrap resamples. SHAP patterns were examined alongside post hoc restricted cubic spline (RCS), interaction, and continuous-K10 analyses. Results XGBoost had a test ROC-AUC of 0.838 (95% CI 0.812–0.861), average precision of 0.692 (0.614–0.765), and Brier score of 0.124 (0.108–0.141). At a development-derived threshold of 0.28, sensitivity was 0.739, specificity 0.846, and positive-class F1 0.658. Calibration slope was 1.03 (0.81–1.28), and intercept was −0.04 (−0.22 to 0.15). Cluster-robust RCS testing suggested nonlinearity ( p = 0.007), with greater uncertainty above approximately 500 min/week. The exploratory MVPA × JSS-4 interaction test yielded p = 0.024. Conclusion In this single-university sample, XGBoost had the highest observed discrimination among the evaluated models. Nonlinear MVPA associations and statistical interaction with sleep disturbance warrant independent investigation. The results do not establish causal effects, an optimal activity dose, clinical utility, or generalizability to other universities.