I read this intetesting page about fit indices in SEM. There are lot. It seems that the RMSEA is one you should always report, but how to choose the other ones? Is there some kind of rule of thumb? Cherrypicking is something I want avoid.
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asked Dec 25, 2015 at 21:47
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1 Answer
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The go-to classic reference for this matter is Hu & Bentler's (1999) paper on fit indexes for SEM. In the paper, they advocate for a "2-index presentation strategy", for which you report an absolute index of model fit, and a relative index of model fit.
Absolute indexes of model fit compare the fit of your model against a perfect fitting model. Recommended absolute indexes include the RMSEA (especially nice, because you can get a confidence interval to perform a test of close fit), and the SRMR. The recommended cutoffs for these two are generally similar; the smaller the better, and < .08 is generally recommended to be considered acceptable, though these guidelines may vary by discipline.
Relative indexes of model fit compare the fit of your model against a "null" model--a deliberately poorly fitting model that is still reasonable (usually that all observed variables are uncorrelated with one another). Recommended relative indexes include the CFI, and the TLI/NNFI (different acronyms, but the same index). Again, the recommended cutoffs for the CFI and TLI/NNI are generally similar; the bigger the better, and > .90 is generally recommended to be considered acceptable.
Note that your model fit index selection and/or calculation might need to change depending on your modelling needs. For example, Little (2013) suggests that you should use a manually amended null model when calculating relative indexes of model fit for longitudinal structural equation modelling. And when comparing groups for measurement purposes, the change in CFI between competing models can be a particularly useful index (Cheung & Rensvold, 2002).
References
Cheung, G. W., & Rensvold, R. B. (2002). Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance. Structural Equation Modeling, 9, 233-255.
Hu, L., Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.
Little, T. D. (2013). Longitudinal structural equation modeling. New York, NY: Guilford Press.
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$\begingroup$ Thank you for your quick response!. I still think it's difficult to choose. What if there is among all the indeces only one absolute and only one relative index that can be interpreted as a good fit. Isn't it cherrypicking if only report these two? But I will accept your answer, because it's very usefull in my exploration of the matter. Thanks. $\endgroup$ Commented Dec 25, 2015 at 23:25
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1$\begingroup$ If you stick to those four, there might be cases when they radically diverge from one another (e.g., one shows good fit, one shows poor fit), but they will be few and far between. You could always stick to just reporting all of those four too, if you'd rather not tempt yourself with the possibility of cherrypicking. $\endgroup$– jsakalukCommented Dec 25, 2015 at 23:27
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$\begingroup$ Last but not least: one means good fit, the other means not so good fit. What would the final conclusion be? A model with a bad fit? $\endgroup$ Commented Dec 25, 2015 at 23:31
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$\begingroup$ Difficult to judge without any numbers/context. $\endgroup$– jsakalukCommented Dec 25, 2015 at 23:33
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$\begingroup$ I have model with RMSEA of 0.04 and a CFI of 0.85. Bad fit or good enough? But I think this should be a new question :-) $\endgroup$ Commented Dec 25, 2015 at 23:39