For a power analysis of a structural equation model, I'm trying to follow the approach outlined in in the following article:
Wang, Y. A., & Rhemtulla, M. (2021). Power Analysis for Parameter Estimation in Structural Equation Modeling: A Discussion and Tutorial. Advances in Methods and Practices in Psychological Science, 4(1), 1–17. https://doi.org/10.1177/2515245920918253
In the paper the authors also give a guide for their online calculator (yilinandrewang.shinyapps.io/pwrSEM/) which is based on R's lavaan packages. In order for it to work it requires the user to input certain parameters such as the factor loadings for the indicator variables (which could be based on theory or previous validation studies).
On page 10 however, the authors mention the following:
"In our scenario, the researcher has a good idea of the likely population parameter values in the model and inputs those values into the parameter table. The researcher sets the factor loading of each indicator of X and Y to .70 (corresponding to a scale reliability of .74 for X and Y), the factor loading of each indicator of M to .80 (corresponding to a scale reliability of .84 for M), and the a, b, and c paths to 0.30, 0.20, and 0.10, respectively."(p.10)
In this example, the model is a basic mediation model where each of the latent variables (X, Y, M) has three indicator variables (fig. 4).
I'm trying to understand how the factor loadings correspond to the scale reliability. E.g. how do the authors convert the set of three factor loadings of .70 to a scale reliability of .74, or vice versa? In previous post here I did not find any equation that represents this relation.