I am testing an SEM model with 6 IVs, 2 mediators, and 3 outcome variables with controls. Sample size is approaching N=500. Here are some fit statistics: NFI=.89; IFI=.91, CFI=.91, and RMSEA=.09. These indices aren't great but are they acceptable/justifiable?
As a data analyst and based on my experience, your NFI, IFI, CFI results are Justifiable and RMSEA is terrible. I am giving this opinion on the base of sample size you reported. Usually of this sample size models achieve good acceptable fit. I don't know why not in your case. May be there are issues in model indices.
Dear Professor Beutell: The hypothesized model or the structural model can be compared with several alternative models (theoretically justified). This comparison can be made based on the criteria suggested by Morgan and Hunt (1994). If the hypothesized model fits the data better, it would be easy to justify these model fit statistics (e.g., CFI, RMSEA), which has also been reported in past studies. The current model fit statistics you reported is acceptable, at least can be reported as ‘mediocre fit’.
Kline, R. B. (2011). Principles and practice of structural equation modeling, 3rd ed. New York, NY: The Guilford Press.
Morgan, R. M., & Hunt, S. D. (1994). The commitment-trust theory of relationship marketing. Journal of Marketing, 58(3), 20-38.
Osman
You are good to go as all fit indices (CFI, NNFI, RMSEA) in a recommended range. However, you can improve your model further by checking co-variances among independent variables and their errors terms. What is your chi-square and degrees of freedom?
Hi everyone! Thanks for all of your helpful suggestions. I have used this advice and revisited the measurement model as well. Here are the new indices based on your feedback: CMIN/DF=2.39, GFI=.95, NFI=.94, IFI=.96, CFI=.96, RMSEA=.056, PCLOSE=.19. This is a big improvement. Best wishes...Nick
Hi Nick, there is a serious debate about cut off values for fit indices. Your model should still have a significant p(chisq, df)? That's to be expected with your sample size, but at least the view of Les Hayduk should be mentioned, which is very skeptical (in some ways radical): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4297459/
As a supplementary note: have you looked at the nornal distribution of the data? Since you seem to be using Amos, it has a serious influence on various coefficients (ML estimators) in case of doubt.
For me, all the model fits are acceptable in term of CFI, NFI and IFI etc. as they are closed to 0.90. However, some researchers have suggested the value closed to or greater than 0.95 but the values closed to 0.90 are also quoted to be accepted. However, I am bit worry about RMSEA value as it is still greater than 0.80. I would like to suggest if you reduce it to 0.08 or lower. Alternatively, it may lead to move up the other values.
The sharing/contribution is beneficial to me as well, thanks to you all
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