The relationship between physical activity and mental health in middle-aged and older Chinese adults: a moderated mediation and cross-lagged model

(1) Physical activity is positively correlated with mental health in middle-aged and older adults; (2) sleep duration mediates the relationship between physical activity and mental health; (3) cognitive function plays a moderating role in both stages of the mediation process; (4) the executive function subdomain exhibits differential moderating effects in middle-aged and older adults compared to memory; (5) longitudinally, cognitive function predicts mental health and positively moderates the relationship between sleep duration and mental health.