I am using a SEM for complex non-normal continuous data (8 factors with 24 indicators (indicators are parcels of items)).
When performing a CFA, CFI=0.976, RMSEA=0.039 (p(RMSEA <= .05)=0.955), SRMR=0.055 which should be OK.
However, when I check the residual covariances (Standardized Residuals (z-scores) for Covariances/Correlations/Residual Correlations) with "Output: RESIDUAL", these values are a 6 times above 4.0 (up to 7.4). I heard this is not acceptable. Could data non-normality cause this? Modification indices are also relatively high (>10) despite low cross-cross loadings (<0.3, in most cases <0.2) when checking with SPSS factor analysis.
If you are not using MLR, I would use it. This estimator is robust to non-normality.
I would do an EFA to see if the CFA model is appropriate for the data.
Melvin C Y posted on Thursday, November 11, 2010 - 2:31 am
Dear Dr Muthén,
this question is related to standardized and normalized residuals. I've read the 2007 technical article. I've large standardized residuals (>2.0) but the normalized figures are much smaller (<1.0). I've a large sample (2000+). I know that values for standardized residual are sensitive to sample size. So a small difference in the correlation residuals will produce a significant standardized residual. Should I be looking at the normalized residual matrix since the formula includes N in the denominator? Is it more appropriate for dataset with large samples?
Normalized residuals are mostly descriptive. Standardized residuals afford testing, but as you say may be too powerful. But, remember that residuals are for finding misspecifications - the overall fit is judged by chi-square. And, remember that even as a tool for finding misspecifications, residuals can be inferior to modification indices because MIs point directly to a parameter in need of change. I would rely more on MIs and see if they point to a problem that is of substantive importance.
Melvin C Y posted on Thursday, November 11, 2010 - 8:53 am
Thanks for this. I agree that the MIs are more straightforward and useful. It's just that I've seen papers and coursework notes reporting the normalized residual matrix and assessing them by the same z test as what is normally done for standardized residuals. So I'm not sure what they have done is correct. I've reviewed a couple of popular SEM texts and standardized residuals seem to be the convention. MIs are also reported but there is increasing importance (e.g., Kline, 2010) for researchers to also report the correlation residuals. The preference is to have a final model that does not contain any significant residuals (>2.0). But this is sometimes not easy especially when you are testing several latent factors. I was intending to use normalized residuals and assess them according to z test. Since the values are always smaller, it is tempting to report normalized residuals as they help to accept the model. Now it seems clear to me that I should use standardized residuals, if I ever decide or am asked to report them.