Linda- I'm sorry if this has been addressed elsewhere, but I am confused as to how standardized residual covariances in a CFA are calculated in Mplus. In a particular analysis that I have, while unstandardized estimates are similar across EQS and Mplus (.260 and .255 respectively), the standardized values (StdYX in Mplus) are not (.609 vs. .254).
It appears to me that the StdYX values in Mplus are standardized based on the variability of the manifest indicator variables and not based on the variability of the estimated residuals. So, the Mplus estimate indicates that Y1 and Y2 are correlated .254 though the relation of the two residuals. Is this correct? Is there a way to obtain the standardized estimate based on the residual variability (as in EQS)? (Other than my manual estimation of dividing .255 by the estimated standard deviations of residuals for Y1 and Y2?)
If there is an argument that the Mplus estimates are to be preferred, is there some citation that I may refer to in order to please a reviewer?
Mplus gives estimates standardized by the estimated variances of the observed variables and the factors. So with residuals for the CFA indicators you standardize using the estimated variances of the observed indicators. This is different than getting a residual covariance standardized by the estimated variances for the residuals - which gives a residual correlation. I assume EQS does the latter. Mplus does not provide this, but we have thought of adding it. The two approaches answer different questions. The Mplus approach answers the question of how large portion of the observed indicator correlation is due to the residuals covarying.
Thanks! I will just calculate and report the residual correlation. The folks at Psych Assessment were (strongly) not supportive of reporting the observed indicator correlation through residuals. I encourage you to add the residual correlation to the Mplus output. I worry that many users probably assume that the StdYX column provides the residual correlation.
I have the same concern like Laura. I’d like to report correlations between the residuals of three latent factors after a fourth factor has been partialed out from their structure. In the standardized output (StdYX) Mplus provides standardizes residual covariances for the parameter I am interested in (so relation between residuals) – their standardization is based on the variability of the manifest indicator variables - like you say above.
If I calculate MANUALLY the standardized value based on the estimated residual variability by dividing the unstandardized parameter estimate for the respective relation by the root squares of the estimated variances of those residuals taken from the output of UNSTANDARDIZED parameters, I am wondering to get the same value provided by Mplus in the StdYX output. Am I doing something wrong? I am using WLSMV for fit the model.
Different from those 2007 postings, the current Mplus version reports the correlation between residuals in the standardized output as you describe it. So the manifest variable variances are not involved in this.