Goodness of Fit (GoF)
Abstract
The goodness of fit (GoF) has been developed as an overall measure of model fit for PLSSEM. 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 GoF may be useful for a PLS multigroup analysis (PLSMGA).
Description
Also see the information on model fit.
"Unlike CBSEM, PLSSEM does not optimize a unique global scalar function. The lack of a global scalar function and the consequent lack of global goodnessoffit measures are traditionally considered major drawbacks of PLSSEM. When using PLSSEM, it is important to recognize that the term fit has different meanings in the contexts of CBSEM and PLSSEM. Fit statistics for CBSEM are derived from the discrepancy between the empirical and the modelimplied (theoretical) covariance matrix, whereas PLSSEM 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). While a global goodnessoffit measure for PLSSEM 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). As a consequence, researchers using PLSSEM rely on measures indicating the model’s predictive capabilities to judge the model’s quality." (Henseler et al., 2014).
Henseler and Sarstedt (2012) explain in detail that the so global goodness of fit (GoF) for PLS by Tenenhaus et al. (2004) does not represent a fit measure and should not be used as such. However, Henseler and Sarstedt (2012) also show that the GoF may be useful for a PLS multigroup analysis (PLSMGA) when researchers compare the PLSSEM results of different data groups for the same PLS path model.
Links
References

Hair, J. F., Hult, G. T. M., Ringle, C. M., and Sarstedt, M. (2017). [A Primer on Partial Least Squares Structural Equation Modeling (PLSSEM)(http://www.plssem.com), 2^nd^ Ed., Sage: Thousand Oaks.

Henseler, J., and Sarstedt, M. (2013). GoodnessofFit Indices for Partial Least Squares Path Modeling, Computational Statistics, 28(2): 565580.
 Tenenhaus, M., Amato, S., and Esposito Vinzi, V. (2004). A Global GoodnessofFit Index for PLS Structural Equation Modeling, Proceedings of the XLII SIS Scientific Meeting. Padova: CLEUP, 739742.