Multiple Regression and SEM

#1
This is largely a theory question. I have been unhappy with my professor's attempt to answer this question for me so I want to get others' opinions.

Given a situation where either could be used justifiably, what would be factors that would lead you to a regression over SEM or vice versa. I guess I'm wondering if doing an SEM analysis is always better than a regression or whether it is only better when there is not one observed criterion variable.
 

fed1

TS Contributor
#2
Hello Krytellan, and thanks for answering so many questions. I am not really expert with SEM but I thought someone should answer since you have made such an effort on other posts.

SEM is essentially a regression with a non identity covariance matrix. The parameterization of the covariance matrix is decided by the causal model or path structure posited by the analyst.

This is almost identical to regression with, say, a mixed model, which is just regression with non identity covariance matrix.

The essential difference (in my narrow view) is that the person using SEM believes that the covariances between observations are caused by something, an observed coavariate or otherwise, while mixed model does not make such inference.

Hope this helps.
 
#3
SEM is essentially a regression with a non identity covariance matrix. The parameterization of the covariance matrix is decided by the causal model or path structure posited by the analyst.
Thanks for taking the time to respond. You know, as I spend more and more time here at Stats Help, I am realizing how much I have not been taught in my graduate studies. It's making me a little nervous.

Can you very briefly explain the concept of an identity covariance matrix? Does that refer to the idea that there is one such way that variables are related? Would that then mean that a non-identity matrix would be one that could be modified based on how variables are assigned to be related (as in SEM)?