Nonlinear Mediation of Parental Phubbing on Child Loneliness: SHAP Interpretability and Double Machine Learning Insights

Objective Grounded in social-ecological theory and parent-child system theory, this study investigates the mechanism by which parental phubbing (excessive smartphone use during parent-child interactions) influences children's loneliness, with a focus on the chained mediation effects of parent-child cohesion and children's social anxiety. Existing research predominantly employs parallel mediation models, overlooking the sequential transmission between parent-child interactions and social development, while traditional regression analyses fail to capture nonlinear relationships in behavioral data. Methods Utilizing scales for parental phubbing, children's loneliness, parent-child cohesion, and social anxiety, we conducted a questionnaire survey with 300 fourth- to sixth-grade students from a primary school in Shanxi Province. Predictive models were constructed using Gradient Boosted Regression Trees (GBRT) and a double machine learning framework, with variable contributions analyzed via SHAP (Shapley Additive Explanations) values, and chained pathways validated through mediation random forests. Results Parental phubbing exhibited a direct effect on loneliness (β = 0.29, 95% CI: 0.21–0.37). The chained mediation effects of parent-child cohesion (β = −0.24) and social anxiety (β = 0.18) were significant (total indirect effect = 0.041), with a nonlinear threshold effect: when parent-child cohesion scores fell below 3.2, the mediation effect intensity increased by 1.7-fold. Conclusion This study reveals a nonlinear dose-response relationship between parental smartphone use and children's psychological distress, providing quantitative evidence for targeted interventions.