Does normalizing observed variables (i.e. bringing them to zero mean and unit variance) influence the fit statistics in SEM? I am running maximum likelihood confirmatory factor analysis with Satorra_Bentler Correction for the measurement model. SB RMSEA is 0.042 (non corrected RMSEA is 0.055) and SRMR is 0.056 which with a sample size of 267 signal good model fit (Hu & Bentler, 1998, 1999) but my SB CFI is 0.92 (non corrected CFI is 0.896) and SB TLI is 0.906 (uncorrected value is 0.877). The latter two values remain under the 0.95 treshold. I'm looking for ways to improve model fit. Already looked at MIs and nothing can be changed. Any suggestions? Can normalization of the observed variables help? Can you direct me to any readings relevant to this question? Thank you for your answers.
Hello Andac,
If, by normalizing, you mean applying a linear transform so that scores on a variable are rescaled to a mean of zero and SD of one, then:
1. Fit indices based on standardized units (e.g., SRMR) will not change.
2. Fit indices that derive from unstandardized units may change.
If, by normalizing, you mean using non-linear transform(s) to make the score distribution for a variable more closely resemble a normal (Gaussian) distribution, then, yes, all of the fit indices could potentially change.
However, if you're asking, will linear transforms wildly affect fit indices in situations wherein you: (a) cannot change the model in any way; and (b) cannot collect any further data, then the answer is "no."
Good luck with your work!
You already have your answer... you seem to be concerned about the cfi and tli being too low. I wouldn't. The cfi tells you how much better is your model than a model in which your variables are uncorrelated. Why do you want to know that?
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