Can you suggest an introduction to structural equation modeling for math majors and mathematicians?
There seem to be a number of topics in science that use mostly standard mathematics, but bury it with a lot of new terminology and non-mathematical ideas. Maybe there is no reasonable way to avoid or even criticize this, since mathematicians also make up new terms all the time. Still, it can be weird and frustrating to have to learn more and more terminology for the same math. "Structural equation modeling" seems to be one of these cases.
My impression is that structural equation modeling is a graph-theoretic generalization of correlations between random variables. Very often in statistics you have a bunch of random variables, hypothesized correlations among some sparse sets of the random variables, and observed correlations among other sparse sets of the random variables. You'd like to fit the hypotheses to to the observations. The fact that the relationships under consideration are sparse makes the question graph-theoretic. The hypotheses chain together in paths through the graph to make predictions that can be compared to the data.
The publications page of Judea Pearl, who is one of the founders of the field, seems to be relatively sane for a mathematical audience. He is a CS professor. In particular, the thesis of his PhD student Carlos Brito, posted on this page, could be a good introduction.