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Message/Author
 Eliana Greenstein posted on Tuesday, April 13, 2010 - 8:53 am
Hi.
I am running an EFA with 12 categorical variables and all load strongly on a single factor (factor loadings range between .771 and .953). However, while my Chi Square is significant and the CFI = .989 and TLI = .987, the RMSEA is .184 and the SRMR is .061. Can you suggest any reason for the high RMSEA? Are there any steps that I should take to try and make it lower? Is it possible that the scale is still valid, even with the RMSEA out of an "acceptable" range?
Thank you.
 Linda K. Muthen posted on Wednesday, April 14, 2010 - 7:49 am
The chi-square p-value should be greater than .05 for good fit. It sounds like you need to modify your model.
 Eliana Greenstein posted on Monday, April 19, 2010 - 8:29 am
Linda,
Thank you for your quick response.
The Chi square p-value being less than .05 can be attributed to the large sample size (n=1285), is there any reason that the CFI and TLI are good indicators of fit, while the RMSEA is not?
Thanks again.
 Linda K. Muthen posted on Monday, April 19, 2010 - 4:47 pm
If chi-square is not good, RMSEA will not be either. A low p-value for chi-square cannot always be attributed to sample size. It is often truly a sign of poor fit. You might instead ask why CFI and TLI are good. This could be because of low correlations among your variables.
 Eddie T. C. Lam posted on Tuesday, September 28, 2010 - 4:19 am
Chi-square is not a reliable "fit index" since it is affected by sample size (it is always significant when N > 200). It is also affected by the complexity of the model (too many variables in one factor, just like your case). Check normality of the data since highly skewed and kurtotic variables would also increase chi-square values.
 Delphine De Smedt posted on Tuesday, February 28, 2012 - 1:22 am
Hi,

We are running a CFA with two factors in Mplus.
As a result we found the following fit indices:

Chi square
value:6959.053
p-value:0.0000
RMSEA:0.130
CFI:0.955
TLI:0.944

All factor loadings were high, ranging between 0.603 and 0.882


Correlations among variables were high.

Can you suggest any reason why the RMSEA is so high? The high ch-square can be attributed to the large sample size (n=7661)


Thank you!
 Linda K. Muthen posted on Tuesday, February 28, 2012 - 10:13 am
I don't think these fit statistics show good fit. I would look at modification indices to seewhat is causing the misfit in the model. You might also consider an EFA to see if your CFA is correct the the data.
 Walter Müller posted on Wednesday, July 18, 2012 - 9:48 am
Dear Ms. Muten,

Im running a CFA with three factors in Mplus (n>1000). As a result I got the following fit indices:

chi-square: 1285 p .00000
CFI: 0.982
TLI: 0.979
RMSEA: 0.093

Factor loadings are very high (.80 - .90) Factor correlations are high aswell (.80)


CFI/TLI are very goog, while RMSEA is not.
chi-square is (unfortunatly) significant.
What do you think? Is the model fit ok? Can your recommend any papers accepting a RMSEA <.10 as an still appropriate model fit or discussing the problem (RMSEA bad, CFI/TLI very goog)?



Thank you very much for your help in advance!
 Linda K. Muthen posted on Wednesday, July 18, 2012 - 11:18 am
I would explore the fit of this model further. You don't say what your sample size is but chi-square and RMSEA both show poor fit and CFI and TLI are similar in that they compare to a baseline model.
 Hannah Wittmann  posted on Wednesday, July 18, 2012 - 11:28 am
My sample size is almost 1200 persons.
 Linda K. Muthen posted on Wednesday, July 18, 2012 - 11:38 am
This is not overly large.
 Xu, Man posted on Tuesday, March 26, 2013 - 11:49 am
The previous posts didn't show their df. I ran into a similar situation, but came across on the web that RMSEA could be artificially high for models with low df - actually it w.

Kenny, D. A., Kaniskan, B., & McCoach, D. B. (2011). The performance of RMSEA in models with small degrees of freedom. Unpublished paper, University of Connecticut.
 Ole Andreas Nordhaug posted on Saturday, April 19, 2014 - 1:26 am
I'm working with PISA data, and I'm using repweights, so i don't get a chi-square or CFI/NFI-estimates, but I get this:

RMSEA Estimate 0.056
90 Percent C.I. 0.053 0.059
Probability RMSEA <= .05 0.000

SRMR Value 0.026

Can the unacceptable RMSEA probability be contributed to my large sample (N=4686), or does the model really have unacceptable fit?

My Mplus course teacher said that RMSEA and SRMR both under 0.06 showed good fit, but I'm unsure because of the probability.
 Linda K. Muthen posted on Saturday, April 19, 2014 - 5:48 am
Please send the full output and your license number to support@statmodel.com.
 Eric Thibodeau posted on Wednesday, July 30, 2014 - 2:00 pm
I'm having a similar problem. I'm running a CFA with one factor with four indicators, and I'm including one covariance between two indicator error variances, as mod indices of the model without the covariance indicated it would dramatically improve model fit. I have a sample size of N=1700. Chi-square is significant but has a very low value. My RMSEA is high, but CFI/TLI and SRMR are in a very good range. Should I be concerned about chi-square and RMSEA?


Chi-Square Test of Model Fit

Value 21.455
Degrees of Freedom 1
P-Value 0.0000

RMSEA

Estimate 0.109
90 Percent C.I. 0.072 0.151
Probability RMSEA <= .05 0.005

CFI/TLI

CFI 0.995
TLI 0.972

Chi-Square Test of Model Fit for the Baseline Model

Value 4429.274
Degrees of Freedom 6
P-Value 0.0000

SRMR

Value 0.007
 Eric Thibodeau posted on Wednesday, July 30, 2014 - 2:06 pm
Also here are my correlations between the indicator variables, some of these are high, some are moderate, is this adding to the strange fit indices I'm getting


Correlations
DEL AGG DIS FIGHT
________ ________ ________ ________
DEL 1.000
AGG 0.775 1.000
DIS 0.485 0.599 1.000
FIGHT 0.541 0.614 0.820 1.000
 Eric Thibodeau posted on Wednesday, July 30, 2014 - 3:20 pm
I just realized now that this is under an EFA discussion and not CFA...oops! Sorry, maybe someone can still answer though. Thanks!
 Bengt O. Muthen posted on Wednesday, July 30, 2014 - 3:52 pm
I would be concerned with the poor chi-square and RMSEA fits. It is quite possible this might not be the best model (e.g, why not 2 factors each with 2 indicators?), but with only 1 df and 4 indicators you have put yourself in a situation where it is hard to know.
 Eric Thibodeau posted on Monday, August 04, 2014 - 9:06 am
Thanks. I tried 2 factors 2 indicators and the fits were terrible, much worse than one factor. All of my indicator measures are very related and could be argued to have significant item overlap and relatedness. I realize that one factor with four indicators and more than one residual covariance is not identified. My mod indices indicated more than one residual covariance which would make a big difference in improving model fit, however, I can't add them and still have an over-itentified model. This CFA was the first step in a larger SEM with this one factor and multiple observed exogenous variables. When I add my first exogenous variable predicting my one factor, I now can add those other residual covariances in my measurement side and be over-identified. When I do this, my fit is excellent. Is this considered bad practice?

Everyone says to do your CFA first, make that good fitting, then begin to add structural components (my observed exogenous variables). However, I can't make my CFA look great on its own (with the residual covariances that I want to add) because I get under-identified quick. Is it OK practice to add exogenous variables and then do more work on the measurement side?

THANKS!
 Bengt O. Muthen posted on Monday, August 04, 2014 - 11:27 am
I think it is bad practice to make a model part identified by borrowing information from other parts. That makes the modeling more susceptible to misspecification in one part influencing many parts.

If you can't get the CFA to fit well, perhaps you want to either try BSEM or simply give up on the latent variable representation and sum up your variables into a single score. Measurement modeling should really be done on carefully constructed items that have been pilot tested.
 Eric Thibodeau posted on Monday, August 04, 2014 - 2:23 pm
Thanks, this has been very helpful. A few follow-up questions. Originally when I ran my CFA with one factor and four indicators, I had a couple of Heywood cases in my modindices, I had a few StdYX E.P.C.'s over 1.0, interestingly those cases had the largest M.I.'s. Any thoughts on what may be happening here?

Another question, it may be that one of my indicators doesn't belong in this CFA...leaving me with one factor and three indicators. Is adding an equality constraint between two factor loadings the only way to make that model over-identified? If that three indicator model looks good, can I remove those equality constraints when I add exogenous predictors?
 Eric Thibodeau posted on Monday, August 04, 2014 - 2:30 pm
These data are also highly positively skewed
 Bengt O. Muthen posted on Monday, August 04, 2014 - 5:10 pm
You may want to ask these questions on a general discussion list like SEMNET.
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