April 23, 2018
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Bayesian SEM (BSEM)
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Structural Equation Modeling


Quoting from Muthén, B. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29, 81-117:

“Traditionally, psychometric models have been concerned with measurement error and latent variable constructs measured with multiple indicators as in factor analysis. Structural equation modeling (SEM) took factor analysis one step further by relating the constructs to each other and to covariates in a system of linear regressions thereby purging the “structural regressions” of biasing effects of measurement error. The idea of using systems of linear regressions emanated from supply and demand modeling in econometrics and path analysis in biology. In this way, SEM consists of two ideas: latent variables and joint analysis of systems of equations. It is argued here that it is the latent variable idea that is more powerful and more generalizable. Despite its widespread use among applied researchers, SEM has still not been fully accepted in mainstream statistics. Part of this is perhaps due to poor applications claiming the establishment of causal models and part is perhaps also due to strong reliance on latent variables that are only indirectly defined. The skepticism about latent variables is unfortunate given that, as shown in this article, latent variables are widely used in statistics, although under different names and different forms.”

Following are some key references on which traditional and expanded SEM analysis in Mplus are based.

  • Asparouhov, T. & Muthén B. (2015). Structural equation models and mixture models with continuous non-normal skewed distributions. Structural Equation Modeling: A Multidisciplinary Journal, DOI: 10.1080/10705511.2014.947375. Download paper. Download scripts.

  • Asparouhov, T. & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling, 16, 397-438. Download paper.

  • Muthén, B. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29, 81-117. Download paper.

  • 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 Unpublished technical report. Download paper.

  • Muthén, B. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54:4, 557-585. Download paper.

  • Muthén, B., Kaplan, (1985). A comparison of some methodologies for the factor analysis of non-normal Likert variables. British Journal of Mathematical and Statistical Psychology, 38, 171-189. Download paper.

  • Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115-132. Download paper.

  • Muthén, B. (1983). Latent variable structural equation modeling with categorical data. Journal of Econometrics, 22, 43-65. Download paper.

  • Muthén, B. (1979). A structural Probit model with latent variables. Journal of the American Statistical Association, 74, 807-811. Download paper.

  • Muthén, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43, 551-560. Download paper.

  • Wheaton, B., Muthén, B., Alwin, D., & Summers, G. (1977). Assessing reliability and stability in panel model. In D. R. Heise (Ed.), Sociological Methodology 1977 (pp. 84-136). San Francisco: Jossey-Bass, Inc. Download paper.

For more information, visit our General Description page.

For more resources see our Structural Equation Modeling paper topic.