I have specified a model in the following form, consisting solely of manifest variables:
A on B C D E; F on B C G H; I on B C I J;
To my surprise, the results for the path coefficients are different from when I calculate each regression model separately. (a) It seems as if correlations amongst all independent variables (B C D E G H I J) are allowed. Is that correct? (b) Why do I get different path coefficients, compared to calculating each regression model separately?
I understand why the fit indices are different. I am just wondering about the path coefficients. After all, in separate regressions (like A on B C D E) H obvioulsy does not influence A either, etc.; i.e., in neither of these cases are there any paths across the single regressions. Which aspect of this model does lead to differing path coefficients, please? Has it something to do with the correlations of the residual variances of the endogenous variables?
Note that your model says that you have the following set covariates:
B C D E G H J;
When you regress A on B C D E H only, you are estimating a mis-specified model because you are saying that G and J don't influence A (if they actually do, the model is mis-specified). Mis-specified models have distorted parameter estimates. Maybe I am misunderstanding what you are doing.