Physical activity and insomnia in adolescents: the chain mediating role of anxiety and short video addiction.

Adolescent insomnia constitutes a prominent public health priority, frequently co-occurring with psychological distress and digital media dependence. This study evaluated the distribution of shared variance among physical activity, anxiety, short video addiction and insomnia symptoms in adolescents. A cross-sectional survey was administered in December 2025 across five Chinese provinces, utilizing a convenience cluster sampling design to recruit 2,144 adolescents (14.8 ± 1.3 years). Structural path analysis was performed using the SPSS PROCESS macro to map the statistical trajectories among the target constructs while concurrently adjusting for key demographic covariates. Bivariate analysis revealed significant baseline correlations across all analyzed constructs. Path modeling indicated that physical activity maintained a significant negative association with insomnia scores (β = - 0.086, p < 0.001). Total covariance analysis decomposed the data into a direct association accounting for 57.72% of the covariation matrix and three indirect pathways encompassing 42.28% of the shared variance. Specifically, the independent indirect pathways via anxiety and short video addiction accounted for 29.53% and 8.72% of the effect size, respectively, while the chain pathway captured a minimal but statistically significant 4.03%. Structural comparisons further confirmed that the hypothesized chain framework outperformed alternative causal configurations, with the baseline model yielding the lowest Akaike Information Criterion (42.35) and Bayesian Information Criterion (68.12). Rather than establishing definitive causal relationships, these cross-sectional findings indicate that elevated engagement in physical activity typically clusters with a reduction in both psychological and technological risk vectors, thereby supporting the integration of structured exercise into adolescent sleep screening frameworks.