Hi, all!
I am trying to do something, and I don't know if it will work exclusively within the blavaan framework (i.e., I may need to modify Stan code and run it outside blavaan). I have a set of manifest variables (individual characteristics) from which I would like to estimate factor scores, and then predict some normally distributed outcomes (health) with both the factor scores and the manifest variables (only X1 here). Pretty bog-standard SEM there. But I would also like to predict the factor scores using a different set of manifest variables (infrastructural) that do not connect to the rest of the SEM.
When I run this model:
'eta1 =~ X1 + X2 + X3
eta1 ~ Y1 + Y2 + Y3
Z1 ~ eta1 + X1
Z2 ~ eta1 + X2'
The effects of eta1, X1, and X2 on Z1 and Z2 (respectively) are substantially different than if I run this model:
'eta1 =~ X1 + X2 + X3
Z1 ~ eta1 + X1
Z2 ~ eta1 + X2'
Specifically, the effects are larger and have less overlap with 0 in the model with a regression model predicting eta1. The resulting path diagram of the model including the regression for eta1 is
I've been parsing the resultant Stan code and am partially on the way to understanding what is happening but not quite there yet. I was thinking someone here might know immediately. I am wondering exactly what is happening under the hood here. And maybe, what exactly is predicting z1 and z2 from eta1? Is it something like the residual of the factor score once accounting for the regression model for eta1?
This diagram seems to imply to me that y1, y2, and y3 are now part of the pathway to predicting z1 and z2, but I don't want them to be. What I want to do is simultaneously estimate the effect of the y_i's on the factor score (so that I'm integrating over all the uncertainty in the factor score) without them being on the path to predicting the z_i's. Is that what is happening here? What would I need to do to make that happen? Do I need to take this outside of the blavaan framework to do this?
Thanks!