Is It Really More Robust? Comparing the Robustness of the Structural After Measurement (SAM) Approach to Structural Equation Modeling (SEM) Against Local Model Misspecifications with Alternative Estimation Approaches

Structural equation models (SEM) or confirmatory factor analysis as a special case contain model parameters at the measurement part and the structural part. In most social science SEM applications, all parameters are simultaneously estimated in a one-step approach (e.g., with maximum likelihood estimation). In a recent article, Rosseel and Loh (2022, Psychol. Methods) proposed a two-step structural after measurement (SAM) approach to SEM that estimates the parameters of the measurement model in the first step and the parameters of the structural model in the second step. Rosseel and Loh claimed that SAM is more robust to local model misspecifications (i.e., cross-loadings and residual correlations) than one-step maximum likelihood estimation. In this article, it is demonstrated with analytical derivations and simulation studies that SAM is generally not more robust to misspecifications than one-step estimation approaches. Alternative estimation methods are proposed that provide more robustness to misspecifications. However, we argue in the discussion section that applied researchers should nevertheless adopt SAM because robustness to local misspecifications is an irrelevant property when applying SAM. Parameter estimates in a structural model are likely estimated without bias because researchers intentionally fit misspecified SEMs. In contrast, SEMs with some empirically driven model modifications will result in biased estimates of the structural parameters.