Model Assumption Violations in Bayesian Latent Mediation Analysis: An Exploration of Bayesian SEM Fit Indices and PPP

This study investigates the effectiveness of Bayesian approximate fit indices and the posterior predictive <i>p</i>-value (PPP) in identifying model assumption violations in latent mediation analysis. We investigate three common forms of model-assumption violations: (1) errors in the measurement model of the mediator, (2) misspecifications in the measurement model of confounders, and (3) the omission of confounders. Additionally, we evaluate the sensitivity of these fit indices to prior specifications, comparing diffuse priors with weakly informative priors. Our findings demonstrate that BRMSEA, BCFI, BTLI, Γ̂, Γ̂adj, and PPP effectively detect misfit with high certainty when sample size is large. Severe misspecifications, such as using standardized total scores for mediators, lead to significant misfit detected by all indices. Including true confounders mitigates the impact of mediator measurement model misspecifications, making these misfits more challenging to detect. Measurement model misspecifications for confounders of the mediator-to-outcome path result in detectable misfit using all indices. Furthermore, all fit indices effectively identify omitted confounders affecting the mediator-to-outcome path, particularly when the confounding effect is moderate or strong. Weakly informative priors have little impact on the variability of the fit indices. These results highlight the utility of Bayesian approximate fit indices and PPP in diagnosing model assumption violations in latent mediation analysis.