Magic Number .95? Or was it .08? A Refresher on SEM Approximate Fit Indices Thresholds for Applied Psychologists and Management Scholars

Asparouhov T. Muthén B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495–508. https://doi.org/10.1080/10705511.2014.919210

Barrett P. (2007). Structural equation modelling: Adjudging model fit. Personality and Individual Differences, 42(5), 815–824. https://doi.org/10.1016/j.paid.2006.09.018

Bentler P. M. (2007). On tests and indices for evaluating structural models. Personality and Individual Differences, 42(5), 825–829. https://doi.org/10.1016/j.paid.2006.09.024

Brown T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). The Guilford Press.

Crede M. Harms P. (2019). Questionable research practices when using confirmatory factor analysis. Journal of Managerial Psychology, 34(1), 18–30. https://doi.org/10.1108/JMP-06-2018-0272

Falk C. F. Muthukrishna M. (2023). Parsimony in model selection: Tools for assessing fit propensity. Psychological Methods, 28(1), 123–136. https://doi.org/10.1037/met0000422

Hancock G. R. Mueller R. O. (2011). The reliability paradox in assessing structural relations within covariance structure models. Educational and Psychological Measurement, 71(2), 306–324. https://doi.org/10.1177/0013164410384856

Hu L. 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

Jackson D. L. Gillaspy J. A. Purc-Stephenson R. (2009). Reporting practices in confirmatory factor analysis: An overview and some recommendations. Psychological Methods, 14(1), 6–23. https://doi.org/10.1037/a0014694

Jöreskog K. J. (1993). Testing structural equation models. In Bollen K. A. Long J. S. (Eds.), Testing structural equation models (pp. 294–316). Sage.

Kang Y. McNeish D. M. Hancock G. R. (2016). The role of measurement quality on practical guidelines for assessing measurement and structural invariance. Educational and Psychological Measurement, 76(4), 533–561. https://doi.org/10.1177/0013164415603764

Kenny D. A. Kaniskan B. McCoach D. B. (2015). The performance of RMSEA in models with small degrees of freedom. Sociological Methods & Research, 44(3), 486–507. https://doi.org/10.1177/0049124114543236

Kenny D. A. McCoach D. B. (2003). Effect of the number of variables on measures of fit in structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 10(3), 333–351. https://doi.org/10.1207/S15328007SEM1003_1

Markland D. (2007). The golden rule is that there are no golden rules: A commentary on Paul barrett’s recommendations for reporting model fit in structural equation modelling. Personality and Individual Differences, 42(5), 851–858. https://doi.org/10.1016/j.paid.2006.09.023

Marsh H. W. Hau K.-T. Wen Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler’s (1999) findings. Structural Equation Modeling: A Multidisciplinary Journal, 11(3), 320–341. https://doi.org/10.1207/s15328007sem1103_2

McCullagh P. Nelder J. A. (1989). Generalized linear models. Springer US. https://doi.org/10.1007/978-1-4899-3242-6

McNeish D. An J. Hancock G. R. (2018). The thorny relation between measurement quality and fit index cutoffs in latent variable models. Journal of Personality Assessment, 100(1), 43–52. https://doi.org/10.1080/00223891.2017.1281286

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

Miles J. Shevlin M. (2007). A time and a place for incremental fit indices. Personality and Individual Differences, 42(5), 869–874. https://doi.org/10.1016/j.paid.2006.09.022

Nye C. D. (2023). Reviewer resources: Confirmatory factor analysis. Organizational Research Methods, 26(4), 608–628. https://doi.org/10.1177/10944281221120541

Preacher K. J. (2006). Quantifying parsimony in structural equation modeling. Multivariate Behavioral Research, 41(3), 227–259. https://doi.org/10.1207/s15327906mbr4103_1

Preacher K. J. Yaremych H. E. (2023). Model selection in structural equation modeling. In Hoyle R. H. (Ed.), Handbook of structural equation modeling (2nd ed., pp. 206–222). The Guilford Press.

Ropovik I. (2015). A cautionary note on testing latent variable models. Frontiers in Psychology, 6, 1715. https://doi.org/10.3389/fpsyg.2015.01715

Shi D. Lee T. Maydeu-Olivares A. (2019). Understanding the model size effect on SEM fit indices. Educational and Psychological Measurement, 79(2), 310–334. https://doi.org/10.1177/0013164418783530

Sivo S. A. Fan X. Witta E. L. Willse J. T. (2006). The search for “optimal” cutoff properties: Fit index criteria in structural equation modeling. The Journal of Experimental Education, 74(3), 267–288. https://doi.org/10.3200/JEXE.74.3.267-288

Steiger J. H. (2007). Understanding the limitations of global fit assessment in structural equation modeling. Personality and Individual Differences, 42(5), 893–898. https://doi.org/10.1016/j.paid.2006.09.017

West S. G. Wu W. McNeish D. M. Savord A. (2023). Model fit in structural equation modeling. In Hoyle R. H. (Ed.), Handbook of structural equation modeling (2nd ed., pp. 184–205). The Guilford Press.

Wulff J. N. Sajons G. B. Pogrebna G. Lonati S. Bastardoz N. Banks G. C. Antonakis J. (2023). Common methodological mistakes. The Leadership Quarterly, 34(1), 101677. https://doi.org/10.1016/j.leaqua.2023.101677

Yuan K.-H. (2005). Fit indices versus test statistics. Multivariate Behavioral Research, 40(1), 115–148. https://doi.org/10.1207/s15327906mbr4001_5