are "overidentified" and "overdetermined" different concepts?

Question

I've recently started learning the Confirmatory Factor Analysis (CFA) method.

The textbook(Timothy A. Brown) shows some examples of model constructs that are either underidentified, just-identified or overidentified. I understand these concepts as whether the number of parameters I'm trying to estimate through CFA is larger-equal-or smaller than the number of data points I've acquired via the covariance matrix.

I thought this concept of overidentified model was equivalent to the concept of overdetermined model concept I picked up from linear algebra and multiple regression classes, so just to clarify I asked my professor whether multiple regression could be considered as "overidentified" model, but he told me it was just-identified. I know that multiple regression in matrix form of Ax=b usually has more rows at the A matrix than the rows in x, which is the coefficients we're trying to estimate via least-squares method.

So I'm inclined to believe that "~identified" and "~determined" are two different concepts. How are these concepts different, given that both compare number of parameters to estimate and the number of data points we have?

Answer 1

I would say you were mostly right with you initial assumption. Overidentified and Overdetermined seem to be similar concepts (whereby ~identified seems to be mostly used in the SEM-Literature (which I am not that familiar with)). But I found a book, in which both are used as equivalent: here

There is some difference in how the concept is interpreted in the context of SEM compared to a regression-context: SEM is interested in the number of moments, while regression is interested in the number of samples (taken from this reddit-discussion )