Solved – Introduction to structural equation modeling

modelingpsychometricsreferencesstructural-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.

Best Answer

I would go for some papers by Múthen and Múthen, who authored the Mplus software, especially

  1. Múthen, B.O. (1984). A general structural equation model with dichotomous, ordered categorical and continuous latent indicators. Psychometrika, 49, 115–132.
  2. 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 Unpublished technical report.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:

  1. Rabe-Hesketh, S. Skrondal, A., and Pickles, A. (2004b). Generalized multilevel structural equation modeling. Psychometrika, 69, 167–190.
  2. 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.

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