## Measurement model vs. SEM without latent variables

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Joined: 11/11/2011

Hi everybody,

I am new to the methodology of SEM, and though I do have a basic understanding of regression and factor analysis, I have not come to grips with one question:
Instead of adding a measurement model to the system of regression equations that contains one or more latent independent variables, could I instead feed the measurement items to the regression equations directly?
Technically I might, of course, but there must be a reason why this is not seen as appropriate. In what sense can the larger system of regression cum measurement equations perform better than a smaller system of regression equations including the measurement items as additional regressors?
To me it seems an (maybe too?) obvious question to pose, but in my (admittedly superficial) glances at SEM monographs (Bollen, Brown) I haven't found that covered. If somebody could give a bit of intuition or hint at helpful literature that would be much appreciated.

Kind regards, Thorsten

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Joined: 07/31/2009
Not sure what you are asking

I'm not clear what this means exactly:
"instead feed the measurement items to the regression equations directly"

Is it possible that you are asking whether the distinction between the measured and various layers of latent variables is somewhat arbitrary? It is, of course, in the sense that all SEMs can be specified in RAM notation using only two matrices: A for asymmetric paths and S for symmetric ones (plus a filter matrix to extract the predicted covariances of only the manifest variables). There may be computational and sometimes conceptual advantages to being more explicit about the distinction between levels of an SEM, a la LISREL model for example. But there exists mathematical equivalence.

That being said, of course there are modes one can fit with latent variables that one cannot with plain multiple regression. The simple factor model is one.

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Joined: 06/27/2011
Why Latent Variables?

I will take a shot at answering your question. Off hand, I can think of three reasons for specifying models with latent variables:

(1) Control for the effects of unreliability (see http://davidakenny.net/cm/psycho.htm);
(2) Proper specification (if the LVs are truly factors, then they should be specified so - this is related to the issue of formative vs reflective measurement);
(3) Proper specification (you answer a very different question when you specify some predictors as LVs, as compared with entering all predictors into a regression equation).

Hope this helps!