No Single Approach Fits All: Testing Two Generations of Structural Equation Modeling Estimation Frameworks

Classic estimation of structural equation modeling (SEM) relies on explicit, closed-form derivatives and Newton-type optimizers like BFGS that use both gradient and curvature information. Although effective in many contexts, this approach can become unstable with small samples, model misspecification, or poor measurement quality. A more recent framework, computational-graph SEM (cgSEM), recasts SEM in a graph-based form with automatic differentiation and adaptive optimizers from deep learning, like Adam, that operate on gradients only. cgSEM’s original work showed that it could reproduce results from classic SEM. However, this equivalence was achieved by using Adam with strict, precision-based stopping rules, similar to those used in many classic SEM implementations, despite Adam being developed with stability-oriented optimization in mind. Thus, it remains unclear how cgSEM performs when Adam is used as intended. We compare classic SEM and cgSEM under maximum likelihood estimation, letting each implement its natural optimization strategy. In simulations, cgSEM showed higher admissible-solution rates and lower small-sample bias under challenging conditions, whereas classic SEM was consistently faster and showed lower large-sample bias with weak indicators. Ultimately, no single approach fits all; framework choice should be guided by the modeling context and which approach is more likely to yield usable results.