XIV. Introduction to Unstandardized Path Diagrams

The procedures which are used to translate unstandardized path coefficients into a variance/covariance matrix are really the same as those outlined for standardized coefficients. Figures showing unstandardized paths are not often published, usually because the researcher is interested in showing the relative magnitude of effects associated with variables in different scales.

However, just as unstandardized coefficients can be helpful in comparing results across studies, the unstandardized coefficients from a structural model can also help communicate which effects from some studies are similar to effects found in other studies.

The logic presented on pages 12-14 of Loehlin can easily be extended to show how you can use a variance/covariance matrix and an unstandardized path diagram to solve for unstandardized regression coefficients. After reading this section of Loehlin's book and going through the math outlined here, I believe you should be able to use a path diagram to produce the formulae for unstandardized regression weights.