CFA - Chi Square and SRMR - Fit Indices

#1
Hello,
I'm running a cfa to examine a scale with 3 correlated factors (subscales) and 14 observed variables (items) and n=79 (which is actually, unfortunately way too small for cfa).

The chi²-test is significant, so actually I should reject the model, but it is recommended to additionally calcute the chi²/df, cause the chi²-test is sensitive too sample size, which means that it often gets significant although the model should not be rejected, when there are BIG samples.

The chi²/df is 1,988 in my case, so still acceptable.

My question is now, does it make any sense to calculate and interprete the chi²/df with such a small sample (n=79)? Or should I trust the significant chi²-test then?

I also read that the SRMR should be used, if the chi²-test is significant and that if the SRMR is smaller than .08 (and there are no huge residuals) the model can be seen as "approximate fit", does that make sense in my case?

I would be so thankful, if anybody could help me, all my research does not bring clearity but sometimes even more possibilties and confusion :/

Thank you so much!
Little Fish
 
#3
I used robust MLR Method, since Mardia's test says there is no multivariate normality.

First I have to correct myself, the ROBUST chi²/df is 10.67 -> which seems absolutely unacceptable of course..

RMSEA is 0.348

And I am not sure how to interprete the CFI, since the robust (right hand column) estimate is 0 (and for TLI even negative?!)
Is that a sign that something went wrong?

Or should I use the "Robust Comparative Fit Index (CFI) with 0.643?
The thing is, I don't understand why there is that "robust" estimate for all the indices, and for CFI and TLI there are additional ones, also called
robust... Maybe you could also help me with that?

User Model versus Baseline Model:

Comparative Fit Index (CFI) 0.762 0.000
Tucker-Lewis Index (TLI) 0.707 -0.922

Robust Comparative Fit Index (CFI) 0.643
Robust Tucker-Lewis Index (TLI) 0.561


Thank you SO MUCH!
 

spunky

Doesn't actually exist
#4
Yeah, this is definitely a bad model. What's considered an "acceptable" model means RMSEA < 0.06 and CFI >0.90 as per the Hu & Bentler (1999) criteria. There's also the issue of your sample size which Barrett (2006) commented on:
 

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spunky

Doesn't actually exist
#6
Mostly yes. The computation of the (sample) TLI could be negative and it essentially implies that the independence model (i.e., the model where all correlations are assumed to be 0) fits the data better than the model you propose. So, yes, it does imply that your model is really bad because it is saying that random noise fits better than your model.

But keep in mind that your sample is tiny compared to what one expects for SEM models. It could also be the case that your model is not too terrible, but you need more data to show it. I guess at this point, you can't really claim anything one way or the other.
 
#7
Okay I see, that sounds really bad.
I now found out, that the model gets that bad, because I removed one univariate outlier.
Before the indices were still far from perfect but not that bad at all: chi²/df = 1,988, CFI = 0.818 TLI = 0.776 RMSEA = 0.144 and SRMR = 0.089.

Is that possible? To me it seems crazy, that the model fit gets way worse with deleting an outlier (usually its supposed to make it better?!)