Comparing correlations -- output vs T...
Message/Author
 Calvin D. Croy posted on Wednesday, June 21, 2006 - 8:56 am
I ran a CFA with 2 factors. I note that the value in the first column of output for Factor2 with Factor1 doesn't match the correlation between the factors provided by the Tech 4 option. However, the value in the output in the far right column under the heading StdYX does match the Tech 4 value.

1. Assuming the value in the Tech 4 output is truly the correlation of the factors, does this mean that the value in the first column to the right of Factor 2 With Factor 1 of the output is really the covariance of the factors and not their correlation?

2.If the values printed in the first column are not covariances and they're not the correlation, could you explain why they're different from the correlations from Tech 4? (I read a reply by Bengt to a similar question where he said that "if the factors are dependent variables the regular output concerns the residual correlation". I need his explanation unpacked a little. I haven't specified the factors to depend on anything in my model.)

Thanks for explaining more about how the "correlations" in the output and from the Tech4 option differ.
 Linda K. Muthen posted on Wednesday, June 21, 2006 - 9:47 am
The value in the first column is a covariance. StdYX is a standardized covariance. The value is TECH4 is a correlation. These two values will be close.

If you have a covariate in the model, the value in the first column is a residual covariance and the standardized value is a standardized residual covariances. The value in TECH4 is a model estimated correlation.
 Liz Shulman posted on Monday, September 29, 2008 - 4:45 pm
Related to this point, in my model I have a latent quadratic growth parameter whose variance has been fixed. Accordingly, there are no covariances estimated between other variables and this quadratic term. However, the TECH4 output reports correlations with this term--how can that be if I have fixed the variance?
 Linda K. Muthen posted on Tuesday, September 30, 2008 - 8:41 am
You probably have covariates in your model in which case you have fixed the residual variance to zero not the variance.
 IW posted on Wednesday, January 03, 2018 - 12:28 pm
Why does the Tech4 correlation table change depending on the model specification? If I'm looking for bivariate correlations between latent and manifest variables, how should I specify the model?
 Bengt O. Muthen posted on Wednesday, January 03, 2018 - 2:31 pm
Tech4 gives the model-estimated values - that's why values change depending on the model.

If Tech4 doesn't give correlations involving manifests, just put a factor measured without error behind the manifest.