When testing for model fit in CFA/SEM, I am examining the estimates for Chi-Square, RMSEA, CFI, TLI, and SRMR. If I get an adequate fit for CFI, TLI, and SRMR but 0.10/0.09 for RMSEA, instead of continuing to modifying the model, can I say an overall adequate fit was found?
For example:
RMSEA - 0.10 [0.09-0.10]
CFI - 0.94
TLI - 0.93
SRMR -- 0.06
OR
RMSEA - 0.12 [0.11-0.13] / RMSEA - 0.09 [0.09-0.11]
CFI - 0.99
TLI - 0.98
SRMR -0.03
Do you continue to modify the model to reduce the RMSEA value?
Also, what should be done next if longitudinal configural invariance is not established for one of any scales in a large study?
Hi Snigdha,
there are different philosophies regarding "tests" of invariance. Camp #1 says that differences should be tested for deviations from the null hypotheses of "no difference" from the same perspective as for any other parameter. Hence, application and consideration of the chi-square test is way to go.
Camp #2 says that we are rather interested in kinds of "degree of differences", hence judging either the difference in fit indices or the descriptive degree of differences.
In my personal perspective, a) one can and should first test for differences. Rejecting significance testing in invariance tests but at the same time conducting them in substantial inferences (e.g., group differences in slopes) is a bit of a contradiction , b) You can test for significance AND regard the degree of the difference at the same time (as you do in any parameter test where statistical significance is differentiated from practical significance.
Tests of differences between models, however, make only sense, when the base line model cleanly fits (from a chi-square perspecite, as the difference between chisquare values is only chisquare distributed when the respective baseline model is non-significant (Yuan, 2004).
Hence, a few questions for you:
1) How does the model exactly look like? Can you post a path diagram?
2) What is the fit of the configural invariance model?
3) What did you test in the various steps?
4) Alter one step resulted in misfit, did you allow for partial invariance?
If I would find complete invariance, I would simply report that and note the absolute differences. If these are strong, than THIS is the respective results. If they are weak I would critically reflect that when going to the substantive parts of the analysis.
Best,
Holger
Yuan, K. H. (2004). On chi-square difference and z tests in mean and covariance structure analysis when the base model is misspecified. Educational and Psychological Measurement, 64(5), 737-757. doi:10.1177/0013164404264853
Hi Snigdha Dutta ;
CFI, TLI, RMSEA and other indexes cut off values was calculated some assumptions. your data may not meet this assumptions. Take a look this papers for more info.
Bests
Article Assessing Model Fit: Caveats and Recommendations for Confirm...
Article A Simple Analytic Confidence Interval for CFI Given Nonnormal Data
Thanks Holger for your insight and Abdullah for the papers.
Here is some more information which will explain my query better.
An example of configural invariance model fit for one of my 8 scales (Warwick-edinburgh mental wellbeing scale):
WLSMV chi-square 1545.41 P
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