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, 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.
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.
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.
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.
I´m 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)?
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?
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.
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?
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.
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?