Comparing Bayesian estimation and structural-after-measurement approaches for structural equation models with latent interactions and complex data structures

Bayesian and structural-after-measurement (SAM) approaches have been developed, in part, to address limitations of conventional estimators in the context of structural equation models (SEMs) with latent interactions. Although both approaches have shown promise in a variety of contexts including small-sample studies, there is very little literature systematically comparing the relative benefits, limitations, and trade-offs among these approaches. In this study, we (a) compared the performance of estimators under each approach in multilevel SEMs with a within-, between-, or cross-level latent interaction and (b) demonstrated the flexibility of SAM approaches by extending and investigating them in partially nested SEMs with latent moderated mediation. The results suggest substantial differences between estimator performance as a function of the type of latent interaction. SAM approaches performed well with a variety of latent interactions in multilevel and partially nested SEMs, while Bayesian approaches, including those with informative priors, struggled with models that included a cross-level latent interaction and were not easily extended to partially nested SEMs. Overall, the results suggest that SAM approaches are a versatile and highly adaptable alternative or complement to conventional full-information estimators. To conclude, we outline estimator considerations based on the SEM type, latent interaction, and data structure.