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Mplus Discussion > Structural Equation Modeling >
 RJM posted on Thursday, September 15, 2005 - 2:14 pm
I would like to specify a model having an induced latent variable, that is, an endogenous latent variable having no indicators and being wholly defined by its predictors. I imagine the code something like as follows, but this is obviously incorrect:

eta1 on x1@1
eta1 on x2;

y1 on eta1 x3 x4;

Is it possible to specify an induced variable using Mplus?
 Linda K. Muthen posted on Thursday, September 15, 2005 - 2:39 pm
I think you are asking about formative indicators. Following is a description from an earlier post by Bengt:

"In some applications it may be more natural to let a factor be defined as being influenced by indicators, rather than influencing the indicators. An example is SES. Mplus handles this modeling by the following model statements.

f by y*;
f on x1@1 x2 x3;

Note that f by y* (that is, freeing the factor loading for the single indicator y) is the same as y on f. f has to be defined by some y - if instead you use the dummy definition

f by y@0;
y on f;

the estimate shows up in f by y."
 RJM posted on Thursday, September 15, 2005 - 2:43 pm
Yes, this is just right. Thank you.
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