Structural equation modeling (SEM) and positive definiteness

This post is from Bob. Mitzi and I were swotting up on structural equation models (SEM) for our class this past Monday at the Modern Modeling and Methods (M3) conference at Fordham University. It was a lot of fun and now I think I understand SEM notation. I really like these applied conferences and this was a group of psychometrician, econometricians, and sociometricians. Many if not most of them thought about models in terms of SEM, so we thought we should figure it out. But I was left with a concern you may be able to help me sort out. The example The first worked example in Ken Bollen’s seminal 1979 textbook on SEM is a study of how industrialization relates to democracy. It comes from his paper, Bollen, Kenneth A. (1979). “Political Democracy and the Timing of Development.” American Sociological Review, 44(4). and was reprised in his book Bollen, Kenneth A. (1989). Structural Equations with Latent Variables. Wiley. I had the pleasure of sitting across from Ken at the invited…