# Goodness of Fit (GoF)

## Abstract

The goodness of fit (GoF) has been developed as an overall measure of model fit for PLS-SEM. 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 (PLS-MGA). Also see the information on model fit.

## Description

"Unlike CB-SEM, PLS-SEM does not optimize a unique global scalar function. Some scholars have traditionally considered the lack of a global scalar function and the consequent lack of global goodness-of-fit measures drawbacks of PLS-SEM, but we do not take this position. 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 (Hair, Hollingsworth, Randolph, & Chong, 2017; Rigdon, Sarstedt, & Ringle, 2017). 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, Sarstedt, & Ringle, 2019; Henseler et al., 2014). While researchers have proposed various model fit measures for PLS-SEM (Schuberth, Henseler, & Dijkstra, 2018; Tenenhaus et al., 2005), their efficacy for identifying misspecified models is highly limited (see Exhibit 6.2 for a discussion of the measures and their limitations). As a consequence, to judge the model’s quality researchers using PLS-SEM rely on alternative measures that assess the model’s predictive capabilities (Shmueli, Ray, Velasquez Estrada, & Chatla, 2016; Shmueli et al., 2019), both in-sample and out-of-sample (Hair, 2020)." (Hair et al., 2022, pp. 92-93).

Henseler and Sarstedt (2013) 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 (see also Hair et al., 2022). 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.

## References

- Hair, J. F., Hult, G. T. M., Ringle, C. M., and Sarstedt, M. (2022).
**A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)**, 3^rd^ Ed., Sage: Thousand Oaks. - Henseler, J., and Sarstedt, M. (2013).
**Goodness-of-Fit Indices for Partial Least Squares Path Modeling**,*Computational Statistics*, 28(2), 565-580. - Tenenhaus, M., Amato, S., and Esposito Vinzi, V. (2004).
**A Global Goodness-of-Fit Index for PLS Structural Equation Modeling**,*Proceedings of the XLII SIS Scientific Meeting*. Padova: CLEUP, 739-742. - More literature ...