The relationship between interpersonal trust, family capital, and physical activity behavior among university students: a cross-lagged study

To explore the interaction mechanism between interpersonal trust, family capital, and physical activity behavior among college students using a cross-lagged study design, providing a theoretical basis for the healthy development of their physical and mental well-being. A longitudinal follow-up survey was conducted among 412 college students in Sichuan Province, using the Interpersonal Trust Scale, Physical Activity Rating Scale, and Family Capital Scale, in two phases over eight weeks from early March (T1) to early May (T2) 2024. (1) The autoregressive path coefficients for interpersonal trust, family capital, and physical activity behavior were 0.51, 0.41, and 0.66, respectively, indicating good stability (p < 0.001). (2) Interpersonal trust at T1 positively predicted family capital at T2 (β = 0.28, p < 0.001), and family capital at T1 also positively predicted interpersonal trust at T2 (β = 0.23, p < 0.001), indicating a mutual influence between family capital and interpersonal trust. (3) Family capital at T1 did not predict physical activity behavior at T2 (p > 0.05), but physical activity behavior at T1 positively predicted family capital at T2 (β = 0.20, p < 0.001), indicating that physical activity behavior is a causal variable for family capital. (4) Interpersonal trust at T1 positively predicted physical activity behavior at T2 (β = 0.16, p < 0.001), while physical activity behavior at T1 did not predict interpersonal trust at T2 (p > 0.05), suggesting that interpersonal trust is a causal variable for physical activity behavior. (5) Family capital mediated the relationship between interpersonal trust and physical activity behavior (α = 0.046), with a confidence interval of [0.014,0.097]. There were no gender differences in the relationship between interpersonal trust, family capital, and physical activity behavior among college students. There was a longitudinal relationship between interpersonal trust, family capital, and physical activity behavior, where family capital and interpersonal trust mutually influence each other. Physical activity behavior was a positive causal variable for family capital, while interpersonal trust was a positive causal variable for physical activity behavior. Additionally, family capital mediated the relationship between interpersonal trust and physical activity behavior.