Model fit CFA/SEM:
Against Fixed Cut-off Values for Fit Indices

by Arndt Regorz, MSc.
July 1, 2025

When assessing the fit of a SEM or CFA in most cases the resulting fit indices (e.g., CFI, RMSEA, SRMR) are compared to cut-off values from the literature. This blog post will show you why that is not such a good idea and what to do instead.

Conventional Cut-off Values for Fit-Indices

When you are running an SEM or a CFA one important step is assessing the model fit. The first option is looking at the results of a model test (chi square test). But in medium to large sample sizes even small differences between model and reality can lead to a significant model test.

Therefore, in addition (or even primarily) fit indices are used to assess model fit. Some of the most common ones are, e.g., the CFI, the RMSEA, and the SRMR.

In the literature there are many suggestions of cut-off values for adequate fit. The probably most cited one (with more than 100,000 citations) is Hu and Bentler (1999). They suggest as possible cut-off values:

  • CFI > .95
  • RMSEA < .06
  • SRMR < .08

But there are other recommendations for cut-off values, e.g. for the RMSEA, too.

Model Characteristics Impacting Model Fit

The simulation studies that have been used to derive cut-off values had only a limited variability of the different possible modeling parameters. That calls into question whether their results generalize to possibly very different SEM or CFA models.

There are a lot of different factors that can impact the performance of different fit-indices for assessing model fit. According to Groskurth et al. (2024) one has to take into account at least these factors:

  • Sample size
  • Type of estimator (ML/MLR, DWLS/WLSMV)
  • Number of indicators
  • Number and distribution of response options (e.g. 5 of 7)
  • Magnitude of factor loadings
  • Factor correlation

Moreover, these factors don’t work independently from each other but can even interact with each other. For instance, some of these factors have a different impact on the cut off depending on the sample size.

This diversity of influencing factors makes the use of the same cut-off values for all kinds of SEM or CFA models highly problematic.

Table Based Cut-off Values

If you run a CFA, then one possibility to get cut-off values for fit indices that are appropriate for the characteristics of your model is using tabled values from Groskurth et al. (2024). Based on simulations they have presented cut-off values depending on a whole range of different model characteristics.

You can find them in their journal article in the Supplementary Online Material (Additional File 5, tables A8, A9, and A10 for CFI, RMSEA and SRMR) of their article.

However, there is only a very limited number of possible combinations of the different factors influencing the cut-off values available in table format. If the specific combination of your model is not represented in these tables, then you need a different solution.

Regression Based Cut-off Values

In addition to presenting tables with cut-off values Groskurth et al. (2024) have also presented an equation based approach. For that they calculated a regression model based on their simulation results for CFAs with different analysis properties. This approach has some conceptual similarity to meta-regression but instead of running a regression based on the results of different primary studies here the regression is run based on simulations with different values for the factors influencing the behavior of fit indices.

With the resulting regression weights you can calculate the estimated cut-off values for many more combinations of influencing factors than are available in table format.

The R code for this regression based approach can be found in Groskurth et al. (2024, Supplementary Online Material, Additional File 6).

[The sample size has to be given in 1,000, i.e., for a sample size of 550 you have to input .55 in order to get realistic results. They have written that in their paper (p. 3910) but in the code example they provide this is easy to miss.]

But there is one important limitation to this approach. In general, regressions don’t perform very well as a prediction tool when being used with predictor values that lie outside of the range of values that have been used to estimate the regression weights.

For instance, Groskurth et al. used as possible factor correlations r = .70, r = .50, and r = .30. If the factor correlation for your study lies outside the range of .30 - .70, then you can’t be sure whether the results obtained from the regression formula are valid for your data.

Simulation Based Cut-off Values

If you can’t use one of the easier approaches mentioned above there remains another option: You can program a simulation study based on the parameters of your specific SEM or CFA model (Groskurth et al., 2024).

However, how to do that is outside the scope of this blog post. For that you need serious programming skills.

References

Groskurth, K., Bluemke, M., & Lechner, C. M. (2024). Why we need to abandon fixed cutoffs for goodness-of-fit indices: An extensive simulation and possible solutions. Behavior Research Methods, 56(4), 3891-3914. https://doi.org/10.3758/s13428-023-02193-3

Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1-55. https://doi.org/10.1080/10705519909540118

Citation

Regorz, A. (2025, July 1). CFA/SEM: Against fixed cut-off values for fit indices. Regorz Statistik. https://www.regorz-statistik.de/blog/cfa_sem_no_fixed_cutoff.html