Overview of Structural Equation Models
The Structural Equation Models (SEM) platform enables you to fit a wide variety of models that can be used to test theories of relationships among variables. The variables in the models can be observed (manifest variables) or unobserved (latent variables). Structural equation modeling is popular in the social and behavioral sciences.
By default, the platform specifies a model with means and variances for all variables. The platform then provides a model-building interface that enables you to see multiple views of the model while it is being built. It also provides some model details during the model construction process that alert you to untenable models prior to running the model.
After you fit one or more models, you can compare the fitted models and two baseline models in the Model Comparison report. The baseline models are an unrestricted model and an independence model. The unrestricted model is a fully saturated model, which fits all means, variances, and covariances of the specified Model Variables without imposing any structure on the data. The independence model fits all means and variances of the specified Model Variables. All covariances among the specified Model Variables are fixed to zero, which leads to a highly restrictive model. You can also choose any of the fitted models in the Model Comparison report to set as the new independence model. This replaces the default independence model in the report and updates the comparative fit indices, providing a more accurate assessment of model fit. See Example of Comparing Multiple Latent Growth Curve Models.
The SEM platform offers multiple estimation methods. By default, it uses Maximum Likelihood (ML) when there are no missing values and Full Information Maximum Likelihood (FIML) when data are missing at random (Finkbeiner 1979). You can also select robust inference with Maximum Likelihood method, which is often referred to as Robust Maximum Likelihood or MLR. The robust version applies a sandwich correction to the standard errors to guard against certain violations of model assumptions. The robust version also rescales the chi-square statistic to prevent against Type I errors. Alternatively, the Model-Implied Instrumental Variables Two-Stage Least Squares (MIIV Two-Stage Least Squares) method provides a noniterative, equation-by-equation estimation approach that is robust to structural misspecification and does not require multivariate normality of predictors. MIIV Two-Stage Least Squares helps contain bias within individual equations and avoids convergence issues that can be associated with ML. It is particularly useful in small samples or when model assumptions are likely to be violated. The method also provides equation-level fit statistics (Sargan tests), which can help identify specific sources of model misfit.
For more information about structural equation modeling, see the CALIS Procedure chapter in SAS Institute Inc. (2025a), Bollen (1989), and Kline (2016).
Note: All models in the Structural Equation Models platform are estimated with a mean structure, which means that a Constant term is included. If you do not want to place a structure on the means of the observed variables, then the means should be freely estimated as in the default model specification.