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The two SEM domains are conceptually distinct, each assuming their own population models with either of the statistical construct proxies, and statistical SEM approaches should be used for estimating models whose construct representations correspond to what they assume. However, SEM approaches have often been evaluated and compared only under population factor models, providing misleading conclusions about their relative performance. This is partly because population component models and their relationships have not been clearly formulated. Also, it is of fundamental importance to examine how robust SEM approaches can be to potential misrepresentation of constructs because researchers may often lack clear theories to determine whether a factor or component is more representative of a given construct. Addressing these issues, this study begins by clarifying several population component models and their relationships and then provides a comprehensive evaluation of four SEM approaches \u2013 the maximum likelihood approach and factor score regression for factor\u2010based SEM as well as generalized structured component analysis (GSCA) and partial least squares path modelling (PLSPM) for component\u2010based SEM \u2013 under various experimental conditions. We confirm that the factor\u2010based SEM approaches should be preferred for estimating factor models, whereas the component\u2010based SEM approaches should be chosen for component models. Importantly, the component\u2010based approaches are generally more robust to construct misrepresentation than the factor\u2010based ones. 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