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st: GSEM results look like piecewise regression results


From   Samantha Brunhaver <[email protected]>
To   statalist <[email protected]>
Subject   st: GSEM results look like piecewise regression results
Date   Wed, 1 Jan 2014 22:54:15 -0800

Hello,

I have Stata/IC 13 and am experimenting with the GSEM command because
I would like to use SEM with both continuous and categorical dependent
variables for my dissertation. I noticed that, in GSEM, the parameter
estimates, standard errors, p-values, etc. that I get are identical to
those I get when I regress each DV on their respective IV's outside of
SEM.

To demonstrate what I mean, I summarize the results of three experiments I ran:

(1) I created a GSEM model with two exogenous observed variables, two
linear mediating observed variables, and a binary endogenous observed
variable, such that the terms on the right in each of the
relationships below regress on the terms on  the left:

exogenous1, exogenous2-->linear1
exogenous1, exogenous2-->linear2
exogenous1, exogenous, linear1, linear2-->binary

The results I got were identical to those I get if I perform these
regressions outside SEM:

regress linear1 exogenous1 exogenous2
regress linear2 exogenous1 exogenous2
logit binary exogenous1 exogenous2 linear1 linear2

(2) I updated my GSEM model, deleting the binary endogenous observed variable:

exogenous1, exogenous2-->linear1
exogenous1, exogenous2-->linear2

The results I got were still identical to these results:

regress linear1 exogenous1 exogenous2
regress linear2 exogenous1 exogenous2

(3) I toggled "GSEM" off and I got different results for #2.

I was wondering if this is to be expected, and if so, what the value
of GSEM is. On a related note, if SEM works by trying to optimize the
covariance matrix, what exactly is GSEM trying to optimize? Even if it
can't treat non-linear equations in the same way, why can't it still
optimize the covariance matrix for whatever linear regression
equations are present in the model?

Thank you very much for your consideration.

Samantha
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