How are the model fit indices calculated by WarpPLS?

WarpPLS is unique among software that implement PLS-SEM algorithms in that it provides users with a number of model-wide fit indices; arguably more than any other SEM software. Three of the main model fit indices calculated by WarpPLS are the following: average path coefficient (APC), average R-squared (ARS), and average variance inflation factor (AFVIF).

They are discussed in the WarpPLS User Manual, which is available separately from the software, as a standalone document, on the WarpPLS web site.

These fit indices (there are several others) are calculated as their name implies, that is, as averages of: the (absolute values of the ) path coefficients in the model, the R-squared values in the model, and the variance inflation factors in the model. All of these are also provided individually by the software.

The P values for APC and ARS are calculated through re-sampling. A correction is made to account for the fact that these indices are calculated based on other parameters, which leads to a biasing effect – a variance reduction effect associated with the central limit theorem.

Typically the addition of new latent variables into a model will increase the ARS, even if those latent variables are weakly associated with the existing latent variables in the model. However, that will generally lead to a decrease in APC, since the path coefficients associated with the new latent variables will be low. Thus, the APC and ARS will counterbalance each other, and will only increase together if the latent variables that are added to the model enhance the overall predictive and explanatory quality of the model.

The AFVIF index will increase if new latent variables are added to the model in such a way as to add multicolinearity to the model, which may result from the inclusion of new latent variables that overlap in meaning with existing latent variables. It is generally undesirable to have different latent variables in the same model that measure the same thing; those should be combined into one single latent variable. Thus, the AFVIF brings in a new dimension that adds to a comprehensive assessment of a model’s overall predictive and explanatory quality.

Starting in version 6.0 of WarpPLS, new indices are available that allow investigators to assess the fit between the model-implied and empirical indicator correlation matrices. These new indices are available from the "Explore" menu option, after Step 5 is completed. They are discussed on page 26 of the WarpPLS User Manual for version 6.0, and on a video clip (links below).

http://www.scriptwarp.com/warppls/UserManual_v_6_0.pdf#page=26

https://youtu.be/YutkhEPW-CE

Also, these new indices are discussed in the following article (see link below for PDF): Kock, N. (2020). Using indicator correlation fit indices in PLS-SEM: Selecting the algorithm with the best fit. Data Analysis Perspectives Journal, 1(4), 1-4.

https://scriptwarp.com/dapj

As a final note, I would like to point out that the interpretation of the model fit indices depends on the goal of the SEM analysis. If the goal is to test hypotheses, where each arrow represents a hypothesis, then the model fit indices are of some importance, but in a limited way. However, if the goal is to find out whether one model has a better fit with the original data than another, then the model fit indices become more important, and are a useful set of measures related to model quality.