In SEM, calculating SE of standardized total effects and indirect effects

[Eric DeRosia]

I'm fitting a SEM model, and everything is fine except the paper's reviewers want standardized total and indirect effects, and I need to report the standard errors of those coefficients.

Here is a bit of the Stata output:

Total effects
-------------------------------------------------------------------
          |                 OIM
          |      Coef.   Std. Err.      z    P>|z|       Std. Coef.
----------+--------------------------------------------------------
Structural|
   C2 <-  |
       C1 |   .4149453   .1280036     3.24   0.001      .1690857

For the standardized coeffient (.169), the output gives no SE. I recognize that's not a bug. According to the v15 manuals, "standard errors of the standardized effects are not reported." I note that as far back as the v12 manuals, it's been the same.

So, I have two questions:
(1) The value of the SE for the standardized coefficient is NOT obvious, right? Stata's choice to not report the SE makes me question the sanity of my sleep-deprived brain.
(2) The z-value wouldn't change when going from the unstandardized coefficient to the standardized coefficient, right? So, could I "back into" a calculation of the missing SE like this? SE of the standardized coefficient = the standardized coefficient / the reported z-value. In the example above, it would be .169/3.24 = .052 . Does that sound like a reasonable way to calculate the SE?

[Phil Bromiley]

You'll increase your chances of a helpful answer by following the FAQ on asking questions.

I don't know why this happens, but I suspect you can get a standardized effect by simply standardizing all the variables before the SEM.