Hi all,
Hopefully this is just a quick question for those of you au fait with CFA in AMOS. I am brand new to this. I'm looking at model (small sample size, yes I know) with 5 latent variables. Two of which could be subjected to second order cfa (however, due to small sample size and lots of latent vars, this makes model fit worse).
My question is two sets of error terms covary (v significantly) on the same latent variable. These pairs of covarying error terms also correspond to their separate latent variables if a second order factor analysis was used they would factor into one of the variables and then 'into' the wider multidimensional variable as it were.
My question is, if I do covary both of these pairs of error terms (which improve model fit etc) I believe I can justify it (re the above, but any help is very valuable with that).
I then am looking to use PROCESS for analysis, so I am wondering, do I then have to adjust anything for that (e.g. delete one of the items for each pair) or do I just analyse with the initial item set?
Thank you!
Hello Amanda,
here is a thread on specifying post-hoc error covariances, their implications, causes, and dangers.
https://www.researchgate.net/post/Theoretical_assumptions_for_correlating_errors_during_SEM#view=5f35166edc797978d53fef05
If you have a small N than the chi-square test on one hand will tend to overreject correct models while at the same time having low power to correctly reject false models. You can apply the so-called swain correction to correct for the first problem but that will probably turn out that the model has problems. Adding error covariances will put make up on it but leave the most probable issue undetected and this be a misspecification of the factor structure.
HTH
--Holger
If I understand correctly, you are conducting a 2nd order CFA with five latent variables, but additional testing indicates that two of these five need an additional correlated error to improve the fit. If this correlated error is relatively large, then I believe this is another way of telling you that these two factors may not be measuring separate things because they are more highly correlated than you predicted.
You can test this by combining the two to create a our-factor model, and test the difference in chi-squares between that and the five-factor model to see if creating the additional factor (i.e., going from four to five factors) significantly increases the fit.
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