Hello Farid,

First, recognize that covariance-based SEM fit indices often do not function well (or even mean quite the same thing) when applied to partial least squares SEM model results, an observation that has been repeated multiple times in the literature (c.f., Hair, Hult, Ringle & Sarstedt, A primer on partial least squares structural equation modeling (PLS-SEM), Los Angeles, CA: SAGE Publications).

Second, in CB-SEM, 0.9 or better is typically the target for the Bentler-Bonnet Normed Fit Index (NFI) [note your query indicated that 0.0941 would be considered a good value, which isn't the case--perhaps the decimal was just mistyped, however].

Third, the NFI has a poor reputation because it invokes no penalty for adding to model complexity (the addition of parameters to a model). See David Kenny's site: https://davidakenny.net/cm/fit.htm, and the quote given below.

Fourth, consider what Hensler, Hubona, & Ray (2016), Using PLS path modeling in new technology research:: updated guidelines, Industrial Management & Data Systems, say about NFI in the context of PLS-SEM:

"The suggestion to use the NFI in connection with PLS path modeling can be attributed to Lohmöller (1989). For factor models, NFI values above 0.90 are considered as acceptable (Byrne, 2008). For composite models, thresholds for the NFI are still to be determined. Because the NFI does not penalize for adding parameters, it should be used with caution for model comparisons. In general, the usage of the NFI is still rare[5]."

Finally, what would an increase in NFI suggest? That your revised model works better compared to the null model relative to how your original model worked (compared to the null model). Could a collinear data set with a mis-specified structure be the "cause" of such shifts? Yes.

Good luck with your work.

Farid Shirazi

The SRMR index has an acceptable range of 0 to 0.08 (Hu and Bentler) (1999). Because the majority of the elements in the SRMR formulation are essentially the mean square error of estimated and observed correlations, the value of 0.08 may be read as follows.

As a result, the NFI produces values ranging from 0 to 1. The greater the fit, the closer the NFI is to 1. NFI values greater than 0.9 generally indicate a good match.

Farid Shirazi NFI should be greater than 0.9. You may also refer to SRMR < 0.09.

Farid Shirazi - The closer to one, the better (above 0.9 should be fine). Please take a look here: https://www.smartpls.com/documentation/algorithms-and-techniques/model-fit

Thank you for sharing this. Yes, I agree that NFI is very sensitive when it comes to the number of parameters in the model impacting the NFI result. As such, this measure is not recommended, but alternatives such as the non-normed fit index (NNFI) that SmartPLS does not currently support.

Regards,

Farid

Farid Shirazi : If you send a short explanation and a "cooking receipt" on how you like to compute the NNFI (and other fit criteria) in PLS-SEM to [email protected] such criteria may be implemented in the next SmartPLS version.

You can have a look at the R package cSEM, there all the fit indices are implemented. We also discuss them in our paper:

Schuberth, Florian; Rademaker, Manuel; Henseler, Jörg (forthcoming). Assessing the overall fit of composite models estimated by partial least squares path modeling. European Journal of Marketing, conditionally accepted for publication.

HTH

Best regards,

Florian

Thank you, Florian, for the info. I look forward to reading your paper.

Regards,

Farid

So that 0.8 is acceptable also!