I don't think you need both. Regression is a special case of SEM (i.e., when the variables are measured without error). Since the assumption of perfect reliability of the measures is usually not realistic, SEM would be preferred. I don't see a reason to use both types of analyses on the same data other than perhaps for illustrative purposes to show the differences due to measurement error.

Christian Geiser , I usually think of the word "regression" very broadly, so including things like Deming regression and also Galton's motivating examples which were about having error in the variables. Do you have a favorite citation for definition of regression? This is just a word-use issue, so happy for people to use them differently, but when teach regression I include dealing with errors in x variables.

Daniel Wright I do not have a favorite definition of "regression", and, as you mentioned, the term can mean different things. In the context of Marcel Grieger 's question regarding "regression vs. SEM", my association for the term "multiple regression" is a linear model of the form

Y = b0 + b1*X1 + ... + b_k*X_k + error

The theoretical notions of regression and SEM might indicate SEM would be preferred.

However, packages for SEM or regression may not be able to estimate all models for SEM or regression. Regression can be seen as a special case for a generalized linear model (or GLMM). In theory you could have a regression model with an error term from any distribution from the exponential family of distributions, like a Poisson distribution (please do not ask for a real-world example).

Maybe some of these models could be estimated using GLMM programs, but I am not sure.

In general, I think in GLMM Structural Equation models with different kinds of error distributions. From this very general idea, all other models are reduced forms (LISREL adopted notion). The mathematical and statistical theory behind this idea as far as I know does not exist (yet), but would include solutions to the Langlang program.

Daniel Wright you are absolutely right, but if you read "regression" in a paper without any further explanation, would you expect that the authors did a total regression/Deming regression? I wouldn't, to be honest.

Rainer Duesing , no, I wouldn't think that, usually (though that was in an example in my class yesterday, so it was probably on my mind). Lots of things come to mind. My point was with both that word and SEM lots of things comes to mind, and it depend how broadly one thinks about them for whether one is a subset of the other. I think it depends what one means by both of those!

Christian Geiser I was indeed referring to a linear regression as you described it. If it is not too much to ask, could you please elaborate why SEM would be preferred in case of measurement error and/or ansence of perfect reliability? So far, I know that latent variables are assumed to consist of manifest indicators measured without error.

I am happy that my rather basic question sparked some interesting exchange. Thank you all for your contributions!

Marcel Grieger I think Christian is much more capable to explain the details, but the crucial point is that you do NOT assume that the indicators are measured without error, but you can directly model the errors and disturbances of the manifest and latent variables. Therefore, you need more than one manifest variable to constitute a latent one, to measure the covariance struchture between them and what is explainable and what unexplained variance.

Marcel Grieger As Rainer Duesing explained, SEM allows you to separate true score (reliable) variance from error variance and to determine the reliabilities of the measured variables. One of the assumptions in conventional OLS regression with manifest variables is that the independent (predictor) variables are measured without error. When this assumption is violated (which it almost always is in the social sciences), the regression coefficients and their standard errors can be biased. This is perhaps the primary reason why SEM would be preferred by many over OLS regression. The regression/path coefficients in SEM are "corrected" for measurement error, provided that your measurement model is set up properly.