Introduction to structural equation modeling I am asked by colleagues some help in this subject, that I don’t really know. They made hypotheses on the role of some latent variables in one study, and a referee asked them to formalize this in SEM. As what they need doesn’t seem too difficult, I think I’ll give it a shot ... for now, I am just looking for a good introduction to the subject!
Google wasn’t really my friend on this.
PS: I read Structural Equation Modeling
With the sem Package in R by John Fox, and this text by the same author. I think this can be sufficient for my purpose, anyway any other references are welcome.
 A: This was the recommended text on the course I took:
P.B.Kline, Principles and Practice of Structural Equation Modeling, The Guilford Press.
It is an introductory text, and not heavily mathematical. 
For a more mathematical, Bayesian, treatment, you could try:
S-Y. Lee, Structural Equation Modeling: A Bayesian Approach, Wiley.
A: Kline's book is excellent.  For a quick intro as a paper see
Gefen, D.  2000.  Structural equation modeling and regression: Guidelines for research practice. CAIS. Volume 4. http://aisel.aisnet.org/cais/vol4/iss1/7/
Hox, J.J. and Bechger, T.M. An introduction to structural equation modeling.  Family Science Review. 11:354-373. http://joophox.net/publist/semfamre.pdf
Lei, P.W. and Wu, Q.  2007.  Introduction to Structural Equation Modeling: Issues and Practical Considerations.  Educational Measurement: Issues and Practice. http://dx.doi.org/10.1111/j.1745-3992.2007.00099.x
Grace, J.  2010. Structural Equation Modeling for Observational Studies.  The Journal of Wildlife Management. 72:14-22 http://dx.doi.org/10.2193/2007-307
See also http://lavaan.org
A: I'm studying SEM at the moment, using LISREL. We're using these two books:


*

*A Beginner's Guide to Structural Equation Modelling

*New Developments and Techniques in Structural Equation Modelling
Dr Schumaker is the instructor on my course. The first book is really good at introducing SEM, as it takes you through the process of model specification, identification, and so forth. While it is based on the LISREL software, I would expect that the general methods and interpretation of results will be independent of software.
A: I would go for some papers by Múthen and Múthen, who authored the Mplus software, especially

*

*Múthen, B.O. (1984). A general structural equation model with dichotomous, ordered categorical and continuous latent indicators. Psychometrika, 49, 115–132.

*Muthén, B., du Toit, S.H.C. & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. Unpublished technical report.

(Available as PDFs from here: Weighted Least Squares for Categorical Variables.)
There is a lot more to see on Mplus wiki, e.g. WLS vs. WLSMV results with ordinal data; the two authors are very responsive and always provide detailed answers with accompanying references when possible. Some comparisons of robust weighted least squares vs. ML-based methods of analyzing polychoric or polyserial correlation matrices can be found in:

Lei, P.W. (2009). Evaluating estimation methods for ordinal data in
structural equation modeling. Quality & Quantity, 43, 495–507.

For other mathematical development, you can have a look at:

Jöreskog, K.G. (1994) On the estimation of polychoric correlations
and their asymptotic covariance matrix. Psychometrika, 59(3),
381-389. (See also S-Y Lee's papers.)

Sophia Rabe-Hesketh and her colleagues also have good papers on SEM. Some relevant references include:

*

*Rabe-Hesketh, S. Skrondal, A., and Pickles, A. (2004b). Generalized multilevel structural equation modeling. Psychometrika, 69, 167–190.

*Skrondal, A. and Rabe-Hesketh, S. (2004). Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models. Chapman & Hall/CRC, Boca Raton, FL. (This is the reference textbook for understanding/working with Stata gllamm.)

Other good resources are probably listed on John Uebersax's excellent website, in particular Introduction to the Tetrachoric and Polychoric Correlation Coefficients. Given that you are also interested in applied work, I would suggest taking a look at OpenMx (yet another software package for modeling covariance structure) and lavaan (which aims at delivering output similar to those of EQS or Mplus), both available under R.
A: Jarrett Byrnes (jebyrnes here) also has his weeklong SEM intro course materials posted here: http://byrneslab.net/teaching/sem/
The course is intended for researchers applying SEMs to biological and ecological data but covers general introductions to SEM concepts, R code, and examples so is likely to be helpful to others.  I found the material very helpful in starting with almost no knowledge of the approach.
A: While only tangent to your goals at this point, if you continue on projects using latent variables I would highly suggest you read Denny Boorsboom's Measuring the Mind. Don't be fooled by the title, it is mainly a detailed essay on the logic of latent variables, and a large critique of classical test theory. I would say it is necessary reading if you are utilizing latent variables in a longitudinal framework. It is only about the logic of latent variables though, it has nothing about actually estimating models.

Do post back with your experiences, I have some of the references given here already, although I would like to expand my library as well. FWIW, Ken Bollen's Structural equations with latent variables was the next on my reading list (although that is only based on my opinion of his scholarly work). 
Besides that I would say I enjoy the work of Bengt Muthén as well. The MPlus software is incredibly popular, and you can see all of the types of analysis that can be accomplished on the Mplus website (link to the user's guide). He also has a series of mp3 postings of his course on statistical analysis with latent variables at UCLA. I haven't listened to them all, but I suspect all are thorough introductions to whatever particular topic is covered for that weeks lecture.
