Intergenerational Transmission of Family Dynamics: A Non-Nested Model Comparison of Gratitude, Depression, and Bidirectional Pathways in Parent-Child Dyads

Abstract This study investigates the bidirectional relationships between family processes, gratitude, and depression in parent-child dyads by comparing three non-nested structural models grounded in intergenerational transmission theory. Using data from 310 Chinese parent-child dyads, structural equation modeling (SEM) tested three pathways: (1) family processes → gratitude → depression, (2) depression → family processes → gratitude, and (3) gratitude → family processes → depression. Model validity, cross-generational effect equivalence, and relative model superiority were assessed using the lavaan and nonnest2 packages in R programming within a unified framework. Results indicated that all models demonstrated significant direct and mediated effects with adequate fit (CFI > 0.90, RMSEA < 0.08), with Model 2 (depression-driven pathways) emerging as superior (CFI = 0.997, RMSEA = 0.013). Wald tests confirmed cross-generational effect equivalence (e.g., family processes → gratitude: W = 0.980, p = 0.322; all p > 0.0167, Bonferroni-adjusted), supporting intergenerational continuity. Crucially, simulation-based sensitivity analysis (N=250-500) not only affirmed robustness of the primary fundings but revealed stronger depression’s effects on gratitude in children than parents (Δβ=0.159-0.164 vs. 0.073), indicating heightened developmental vulnerability previously undetectable in the original sample. Results establish depression's pivotal role in disrupting family functioning and emotional well-being across generations, suggesting parental mental health interventions could disrupt cycles of familial dysfunction. Methodologically, this study advances the application of lavaan and nonnest2 packages for non-nested and nested model comparisons, offering a robust tool for evaluating competing theoretical frameworks. Full R code and simulated datasets are provided for replication and further research use.