The first I know of to show how this is done in Lisrel (or any other software) by hand I think was John Loehlin, although others have tried it algeblraeically too; I'll send a few pages from his book.
It's pretty much by starting with some 'wild' guesses, for each path coefficient, then moving them up and down, one at a time, and see whether the implied correlations drift away from the sample correlations or not. This is tricky, of course, because the one-at-a-time approach assumes that path coefficient values are independent, whereas they are not really. But it's a good exercise.
For going from a set of path coefficients to the model implied correlational matrix, one simply uses the 'tracing rule' of Sewall Wright, take a look at Dave Kenny's example: http://davidakenny.net/cm/tracing.htm
It is easy to use. Add in the program all traits and you can select the character which will be used as Y factor and other factors which were used for calculating path coefficient then save the results.
Thank you for sending the program. I would like to learn the method behind the softwares. When we have 3 variables it is easy to solve. But when we have more than 3 variables I don't know how it works. Could you please help me to learn the method? I want to know how I can solve the problem by hand.
there are 2 methods to solve it. Doolittle method and another method in book of
Steel, R.G.D. and J.H. Torrie (1981). Principles and procedures of statistics, a biometrical approach. 2nd ed. by Mc Graw-Hill International Book Company, Singapore, 633 p.
Also, in the book of Singh as I remember explained it in detail