I was studying a little bit more SEM, specially considering full SEM, where you add latent variables with observable variables in structural modeling (more in terms of path analysis, not construct validity or other psychometric uses).
So... in full SEM you can add an endogenous variable toghether with its exogenous variables, which is interesting, because you are able to account for measurement error in an even deeper level, rather than just adding scores as observable variables. The problem is that sometimes you might find out that there are dependent items across independent measures. For example, I might find out that there are items from a self-efficacy inventory that are correlated with an item or two from a personality measure. It is interesting, though it actually impacts model fit. If you work with too many latent variables you end up adding a lot of measurement error as well, that might not be relevant for the multivariate model, but only in a construct level analysis. A part of me says that "yes... accounting for every error sounds actually more realistic and latent variables are what they are: complicated and highly fluctuating elements of a subjective reality."
Still, adding latent variables in the way full SEM considers sounds more like an approach from Classical Test Theory. One alternative that I tend to use is to estimate in mirt and other packages person location and add it to the model as observable variable for every measure. IRT has many advantages compared to CTT, but I still miss the possibility of including measurement error in the model. So how could I work with irt estimates in lavaan and mplus, while also including measurement error in the model in the same way?
After those reflections I'd like to bring up a discussion also on: how relevant do you think it is to add measurement error (item level) to a path analysis model?
I'd like to say I'm sorry for my english for such a complicate question. Also, in terms of knowledge, that's the time when I really miss some more background in statistics as my base is in psychology... Looking forward to read some interesting opinions around here on SEM.