Looks like my answer got scrapped, for attaching a chapter; the answer is simple: one can move from correlations to path coefficients either: 1. Algebraically, following the tracing rule below, OR 2. by starting with some 'good guess' values', and derive for those guesses the model implied correlations, using the same tracing rule below, then change these path coefficients 1-at-a-time up, then down, and see whether the model implied correlations depart from the sample ones or not; this approach was shown by Loehlin (2005), in his ch. 2 (I can email it, ask for it).

For example, for a latent/factor with 3 reflective/effect indicators, the latent causes all 3, and if no correlation is allowed between the residuals of these 3 indicators, then the correlation between any 2 of them HAS TO BE the product of their loadings, because one can 'go from' 1 to another only through the latent (no other path is possible).

Loehlin, J. C. (2004). Latent variable models: An introduction to factor, path, and structural equation analysis. Mahwah, NJ: Lawrence Erlbaum.

For the tracing rule check David Kenny's example http://davidakenny.net/cm/tracing.htm .

Dear Emil Coman,

Thanks for answering.

Could you please send me that chapter?