effectsize::interpret_cfi(0.99, rules="byrne1994")[1] "satisfactory"
(Rules: byrne1994)effectsize::interpret_cfi(0.99, rules="hu&bentler1999")[1] "satisfactory"
(Rules: hu&bentler1999)SEM notes
Effect size interpretation
Standard rules of thumb
The traditional cutoffs are implemented in interpret_* functions in package effectsize.
References (copied from ?effectsize::interpret_cfi)
* Awang, Z. (2012). A handbook on SEM. Structural equation modeling. (RMSEA)
* Byrne, B. M. (1994). Structural equation modeling with EQS and EQS/Windows. Thousand Oaks, CA: Sage Publications. (CFI, RMSEA, TLI, SRMR)
* 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. (CFI, TLI)Dynamic cutoffs
Traditional cutoffs have problems.
The results showed that traditional cutoffs have very poor sensitivity to misspecification in one-factor models and that the traditional cutoffs generalize poorly to one-factor contexts. As an alternative, we investigate the accuracy and stability of the recently introduced dynamic fit cutoff approach for creating fit index cutoffs for one-factor models. Simulation results indicated excellent performance of dynamic fit index cutoffs to classify correct or misspecified one-factor models and that dynamic fit index cutoffs are a promising approach for more accurate assessment of model fit in one-factor contexts. (McNeish & Wolf, 2022)
Dynamic cutoffs have been offered as a solution: shiny app implementation at https://dynamicfit.app/ - based on the R package dynamic (Wolf & McNeish, 2023).
A tutorial on using dynamic fit indices: Palisek et al. 2025 in Collabra.
References
* McNeish, D. & Wolf, M. G. (2023). Dynamic Fit Index Cutoffs for Confirmatory Factor Analysis Models. Psychological Methods, 28 (1), 61-88. https://doi.org/10.1037/met0000425
* Palíšek, P., Chvojka, E., & Literová, A. (2025). Abandon All Thumbs Ye Who Model: An Up-to-Date Tutorial on Fitting CFA Models. Collabra: Psychology, 11(1). https://doi.org/10.1525/collabra.147248
* Wolf, M. G. & McNeish, D. (2023). dynamic: An R package for deriving dynamic fit index cutoffs for factor analysis. Multivariate Behavioral Research, 58 (1), 189-194. https://doi.org/10.1080/00273171.2022.2163476Cutoffs can be dependent on estimation method
Another consideration: fit indexes seem to behave differently if ordinal variables are used, and/or with diagonally weighted least squares (DWLS) estimator.
The results of a simulation study are presented to show that appropriate cutoff values for DWLS estimation vary considerably across conditions. Finally, regression equations are described to aid researchers in selecting cutoff values for assessing the fit of DWLS solutions, given a desired level of Type I error” (Nye & Drasgow, 2011, 165 citations in WoS as of 20.01.2026)
The results showed that DWLS and ULS lead to smaller RMSEA and larger CFI and TLI values than does ML for all manipulated conditions, regardless of whether or not the indices are scaled. Applying the conventional cutoffs to DWLS and ULS, therefore, has a pronounced tendency not to discover model-data misfit. (Xia & Yang, 2018, 1317 citations in WoS)
Estimation methods had substantial impacts on the RMSEA and CFI so that different cutoff values need to be employed for different estimators. In contrast, SRMR is robust to the method used to estimate the model parameters. (Shi & Maydey-Olivares, 2019, 290 citations in WoS)
References
* Nye, C. D., & Drasgow, F. (2010). Assessing Goodness of Fit: Simple Rules of Thumb Simply Do Not Work. Organizational Research Methods, 14(3), 548–570. https://doi.org/10.1177/1094428110368562
* Xia, Y., & Yang, Y. (2018). RMSEA, CFI, and TLI in structural equation modeling with ordered categorical data: The story they tell depends on the estimation methods. Behavior Research Methods, 51(1), 409–428. https://doi.org/10.3758/s13428-018-1055-2
* Shi, D., & Maydeu-Olivares, A. (2019). The Effect of Estimation Methods on SEM Fit Indices. Educational and Psychological Measurement, 80(3), 421–445. https://doi.org/10.1177/0013164419885164Categorical indicators
WLSMV (a.k.a. DWLS) estimator is suitable for ordered categorical indicators and and has less stringent sample size requirements compared to alternatives (Brown, 2015). With DWLS, Brosseau-Liard and Savalei (2014), recommend using robust corrections to the fit indices (CFI, TLI, RMSEA, and SRMR).
References
* Brosseau-Liard, P. E., & Savalei, V. (2014). Adjusting Incremental Fit Indices for Nonnormality. Multivariate Behavioral Research, 49(5), 460–470. https://doi.org/10.1080/00273171.2014.933697
* Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press. [ ISBN 978-1-4625-1536-3]Invariance testing
Chen (2007) recommends the following cutoff values for noninvariance:
for metric invariance (testing for equality of loadings), a CFI decrease of .010 or greater along with an RMSEA increase of .015 or greater or an SRMR increase of .030 or greater;
for scalar invariance (testing for equality of intercepts), a CFI decrease of .010 or greater combined with an RMSEA increase of .015 or greater or an SRMR increase of .010 or greater. Scaled chi-square and df are reported.
References
* Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling, 14(3), 464–504. https://doi.org/10.1080/10705510701301834