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I did some CFA analyses (using R package Lavaan) on several scales in order to check the unidimensionalities. If I understood well scale 5, 6 and 7 can be considered a good fit because of the RMSEA < 0.08 and the CFI and TLI > 0.90. My question is how to interpret the fit of the first 4 scales. The RMSEA looks good, but the CFI and TLI don't. Am I allowed to say something like "almost a good fit"?

Scale   N       R2      χ2          df  SRMR    RMSEA   RMSEA con.interv.   CFI     TLI
1       1673    0.18    1470.71***  434 0.038   0.038   0.036   -   0.040   0.85    0.83
2       1672    0.19    597.81***   152 0.04    0.042   0.038   -   0.045   0.87    0.85
3       1675    0.16    586.93***   170 0.038   0.038   0.035   -   0.042   0.84    0.82
4       1677    0.25    427.43***   90  0.04    0.047   0.043   -   0.052   0.91    0.89
5       1677    0.24    280.65***   90  0.031   0.036   0.031   -   0.040   0.93    0.92
6       1670    0.26    175.35      54  0.03    0.037   0.031   -   0.043   0.95    0.93
7       1679    0.25    289.79***   104 0.03    0.033   0.028   -   0.037   0.95    0.94
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  • $\begingroup$ Well, I suppose the scale number six is the only one that you can consider as having good-fit considering Kline's standard (a non-significant chi-sqr). In general I tend to use the other indices to compare fit btw different models. You can say that scale 7 has a slightly better fit than the scale 4. You can also run a comparative anova in R to check whether this difference is statistically significant. $\endgroup$ – lf_araujo Jan 6 '16 at 5:26
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A CFI of 0.9 is generally considered to not be very good (nowadays?). So saying that a CFI that is below 0.9 is "almost a good fit" is (IMHO) stretching the truth somewhat.

So why do you have good RMSEA and poor CFI? It's because the two indices test fit in different ways. RMSEA is based on chi-square - lower chi-square means lower RMSEA. The CFI tests fit by comparing with the null model. If your variables are not highly correlated, then your null model doesn't have such bad fit. If your null model doesn't have bad fit, it's hard for the fit to be much better. But that means that there isn't a lot of covariance to be explained by the model, hence a good RMSEA.

The poor CFI and good RMSEA means that you have poor data. Essentially, if your variables are not reliable, your RMSEA will be better, your CFI will be worse.

Here are a couple of papers that might be helpful:

http://www.tandfonline.com/doi/abs/10.1080/10705519609540052 https://www.researchgate.net/publication/221986550_A_time_and_a_place_for_incremental_fit_indices

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