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Re: st: interaction in SEM

From   Stas Kolenikov <>
Subject   Re: st: interaction in SEM
Date   Wed, 7 Dec 2011 11:13:14 -0600

On Wed, Dec 7, 2011 at 10:01 AM, Zhi Su <> wrote:
>  Thanks for the suggestion. Here t is an observed dummy variable.
>  I have also looked into -gllamm-, but found it is hard to understand
> the manual. So I turn to -sem-. Since -sem- does not support nonlinear
> latent varaible, is there any examples for using -gllamm- to estimate
> model as mine? It is better the example has the codes, results and
> explanation for the codes and recults.

You'd have to look at the manual. With some exceptional luck, you
might find an example on website, but your model is a
rather non-standard one, so you may or may not be able to find
anything convincing.

With -gllamm-, you would need to -reshape long- your data into one
outcome (or indicator) per line, nested in your original observations,
and create the variables that would provide the match between your
latent, and your outcomes and indicators. For the indicators -a1- and
-a2-, you will have dummy variables identifying the (reshaped long)
observations that came from these indicators. Their coefficients will
be the loadings in the measurement model. For the outcome -Y-, you'd
have to have a dummy that identifies this variable for -gllamm-, and
its interactions with -t- and -x-. You would also need to put its
interaction with -t- into the equation for the latent variable, so all
in all you will have something like

eq AA : dummy_for_a1 dummy_for_a2 dummy_for_y_times_t
gllamm dummy_for_a1 dummy_for_a2 dummy_for_y dummy_for_y_times_t
dummy_for_y_times_x , id( original_observation) eq( AA )

>  And why do you think my model can not be identified?

Just a gut feeling. If you had three or more indicators of A, I would
not have issues. The factor models with two indicators per factor are
only identified if there are more than one factor with correlations
between them, however, you only have one latent variable. If the model
is not identified, a way to force identification is to impose
constraint, e.g., the loadings of -a1- and -a2- are the same, or the
loadings sum up to 1, etc.

Stas Kolenikov, also found at
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