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I added data (33 observed variables, 8 latent variables, all are Likert scales) and ran CFA. Sample size is 618 respondents. A result was many fit indices (Chi-squre/DF, CFI, GFI, AGFI, NFI, NNFI, RMSEA, SRMR, and Hoelter's) are acceptable, except P-value. I modified my CFA model many times (about 11 times) by followed modification indices that suggested by a software. However, the P-value is still less than 0.05.

My question: is that acceptable if all fit indices are good, but the P-value is less than 0.05?

CFA model modification progress

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  • $\begingroup$ Probably, yes. The reason other fit indices exist is because of problems with chi-square. But I'd be happier saying that if you actually said what the values were. $\endgroup$ – Jeremy Miles Nov 6 '16 at 3:08
  • $\begingroup$ Also, when you ask a question, check and double check the numbers. Presumably you mean 0.05, not 0.5. $\endgroup$ – Jeremy Miles Nov 6 '16 at 3:09
  • $\begingroup$ Thank you very much for the answer. The fit indices were Chi-squre/DF, CFI, GFI, AGFI, NFI, NNFI, RMSEA, SRMR, and Hoelter's. $\endgroup$ – Pakvalit Kurkoon Nov 6 '16 at 13:01
  • $\begingroup$ Ignore chi-square/df, GFI, AGFI and Hoelters, and then tell me the actual values of the others. $\endgroup$ – Jeremy Miles Nov 6 '16 at 19:42
  • $\begingroup$ I uploaded my fit values as a picture file above, but this one, I've tried to push p-value to pass 0.05. $\endgroup$ – Pakvalit Kurkoon Nov 7 '16 at 5:04
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If your p-value is 0.05, that means that assuming the null hypothesis is true, then the probability of you getting the above results is 5%. So effectively, a lower p-value is better.

So I wouldn't worry about your p-value, as it looks good. Simultaneously your CFI, GFI and AGFI are increasing, while RMSEA is decreasing, which are all good signs.

You have to find that optimum region where the p-value is still low, while the CFI,GFI and AGFI are reasonably high, and it looks like you have reached it.

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    $\begingroup$ This is the opposite of true. Lower p-value indicates that the model is unlikely to have generated the data. $\endgroup$ – Jeremy Miles Apr 11 at 2:53

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