R-squared change approaches in Hayes (2021)

[Santiago Garcia]

Hi lavaan group, could someone translate "Approach 3: Direct matrix calculation of 𝑅2𝑅𝑒𝑑𝑢𝑐𝑒𝑑" and "Approach 4: Specifying ξ 2 as a saturated correlate in the reduced model" from Hayes (2021) into lavaan syntax for SEM models?
Two examples using data=HolzingerSwineford1939 would be really appreciated. 
Hayes T. provides the Mplus code only and I am not able to use that to follow the procedure within the lavaan environment. 

Hayes, T. (2021). R-squared change in structural equation models with latent variables and missing data. Behavior Research Methods, 1-31. https://doi.org/10.3758/s13428-020-01532-y

Thank you very much.
Sant

[Terrence Jorgensen]

could someone translate "Approach 3: Direct matrix calculation of 𝑅2𝑅𝑒𝑑𝑢𝑐𝑒𝑑" and "Approach 4: Specifying ξ 2 as a saturated correlate in the reduced model" from Hayes (2021) into lavaan syntax for SEM models?

Hayes T. provides the Mplus code only 

The author provides R functions in the appendices for Approach 3, with examples of how to use them in 3 R syntax files (using lavaan) in the electronic supplementary materials (ESM 6 7 and 8).

Approach 4 simply replaces a regression path with a covariance.  So if your model has 2 latent predictors "ksi1" and "ksi2" of a latent outcome "eta":

eta ~ ksi1 + ksi2

ksi1 ~~ ksi2 # estimated by default using sem(), or set auto.cov.lv.x=TRUE

Then you would compare that R-squared with one from an equivalent model where ksi2 is not a predictor (but is still correlated with eta's residual):

eta ~ ksi1

ksi2 ~~ ksi1 + eta

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen