New Context-Specific Fit Criteria to reveal additional Insights in Structural Equation Modeling

Model (mis-)specification in structural equation modeling can cause researchers to arrive at wrong conclusions or missed insights. There are still contradictory results on how well fit criteria can detect misspecification. In two simulation studies and from empirical examples, we reveal two things. First, recommended fit criteria combinations only marginally cover model (mis-)specification because they still accept many misspecified models or reject too many correctly specified models. Second, the ability of fit criteria to detect (mis-)specification differs between confirmatory factor analysis and covariance-based structural equation modeling and is also subject to data and model characteristics. Therefore, we develop context-specific criteria combinations, which accept more correctly specified models than previous recommendations while rejecting the vast majority of misspecified models. Thus, researchers do not lose important insights but gain additional insights from their data. Beyond, we provide a tool to guide researchers on the appropriate/optimal selection of criteria combinations.