Thereby, it is more comprehensively possible to mimic CB-SEM via the PLSc-SEM approach or to compare the results from the two approaches. Hence, when using PLSc-SEM for a path model that only includes reflectively measured constructs (i.e., common factor models), one may be interested in the model fit. However, when mimicking CB-SEM models with the consistent PLS (PLSc-SEM) approach, one also mimics common factor models with the PLS-SEM approach. Hence, they are inappropriate for PLS-SEM. In contrast, the outer residuals of composite models are not required to be uncorrelated.

For example, certain fit measures assume a common factor model, which requires uncorrelated outer residuals. More specifically, LohmГ¶ller (1989) states that some fit measures imply restrictive assumptions on the residual covariances, which PLS-SEM does not imply when estimating the model. But he states that they have been introduced to provide a comparison to LISREL results rather than to represent an appropriate PLS-SEM index. LohmГ¶ller (1989) already offers a set of fit measures. So far, these criteria usually should not be reported and used for the PLS-SEM results assessment.

SmartPLS provides them but believes that there is much more research necessary to apply them appropriately. Even though, some researchers started requesting to report these new model fit indices for PLS-SEM. The proposed criteria are in their early stage of research, are not fully understood (e.g., the critical threshold values), and are often not useful for PLS-SEM. Researchers should be very cautious to report and use model fit in PLS-SEM (Hair et al.

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