However, Henseler and Sarstedt (2012) also show that the GoF may be useful for a PLS multi-group analysis (PLS-MGA) when researchers compare the PLS-SEM results of different data groups for the same PLS path model. (2004) does not represent a fit measure and should not be used as such. Henseler and Sarstedt (2012) explain in detail that the so global goodness of fit (GoF) for PLS by Tenenhaus et al. As a consequence, researchers using PLS-SEM rely on measures indicating the model’s predictive capabilities to judge the model’s quality." (Henseler et al., 2014). While a global goodness-of-fit measure for PLS-SEM has been proposed (Tenenhaus et al., 2004), research shows that the measure is unsuitable for identifying misspecified models (Henseler and Sarstedt, 2012 see Chapter 6 for a discussion of the measure and its limitations). Fit statistics for CB-SEM are derived from the discrepancy between the empirical and the model-implied (theoretical) covariance matrix, whereas PLS-SEM focuses on the discrepancy between the observed (in the case of manifest variables) or approximated (in the case of latent variables) values of the dependent variables and the values predicted by the model in question (Hair et al., 2012a). When using PLS-SEM, it is important to recognize that the term fit has different meanings in the contexts of CB-SEM and PLS-SEM. The lack of a global scalar function and the consequent lack of global goodness-of-fit measures are traditionally considered major drawbacks of PLS-SEM. "Unlike CB-SEM, PLS-SEM does not optimize a unique global scalar function. The GoF may be useful for a PLS multigroup analysis (PLS-MGA). However, as the GoF cannot reliably distinguish valid from invalid models and since its applicability is limited to certain model setups, researchers should avoid its use as a goodness of fit measure. The goodness of fit (GoF) has been developed as an overall measure of model fit for PLS-SEM.
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