How does Amos compute squared multiple correlations?

Amos computes a squared multiple correlation for each endogenous variable using the formula

Formula for the squared multiple correlation ,

where sigma hat squared for the endogenous variable is the estimated (implied) variance of the endogenous variable and sigma hat squared for the residual variable is the estimated (implied) variance of the associated residual variable.

For example, in the following path diagram

Path diagram with knowledge, value and satisfaction predicting performance

the squared multiple correlation for performance is estimated as

Formula for the estimated squared multiple correlation .

It is not clear how to interpret squared multiple correlations in nonrecursive models. Alternative formulas for estimating the squared multiple correlation have been proposed. (See the references below.)

References

Bentler, P., & Raykov, T. (2000). On measures of explained variance in nonrecursive structural equation models. Journal of Applied Psychology, 85(1), 125-131.

Jöreskog, J.G. (October 2, 1999). What is the interpretation of R²? (http://www.ssicentral.com/lisrel/techdocs/WhatistheinterpretationofR2.pdf)