Margins of latent variable in SEM

[Chris Prosser]

Hi all,

I'm wondering if it's possible to estimate the predictive margins and average marginal effects etc of a latent variable in a structural equation model.

To give you a simple simulated example, say I've got 2000 observations of a variable y that is affected by an unobserved variable U, which is measured through five variables x1-x5, and a few observed covariates z1-z3

set obs 2000
drawnorm U z1 z2 z3

forvalues x = 1/5 {
gen x`x' = U + rnormal()
}

gen y = U + z1 + z2 + z3 + rnormal()

Then I estimate my model like so:

sem ///
(LatentU -> x1 x2 x3 x4 x5) ///
(z1 z2 z3 LatentU -> y)

I know I can estimate the predictive margins of my z variables, with Stata integrating over the latent variable, like so:

margins, at(z1=(-1 0 1))  predict(xb(y))

But what I want to do is estimate the margins of the latent variable itself, i.e.

margins, at(LatentU=(-1 0 1))  predict(xb(y))

But when I do that, Stata tells me "variable 'LatentU' not found in list of covariates"

Is there any way of doing this? Or is there some reason doing this would be a bad idea? I can imagine the calculations of the standard errors are potentially quite complicated but can't see an obvious reason why it wouldn't be possible in theory, but I might be missing something.

Thanks for any help!

Chris

[Francesco Visconti]

Dear Chris,

I have a similar issue (I want to plot the marginal effects of a latent variable). Did you come up with a solution?

Thanks for your attention.

Best regards,

FV