Structural Equation Modeling


Structural equation models (SEMs) refer to a broad class of statistical models that have two components: a measurement component that relates latent (or unobserved) variables to observed indicators and a structural component that captures direct effects, if any, of latent or observed variables on each other. As such, SEMs provide a framework for addressing measurement error and for specifying systems of equations that correspond with theory. This entry provides an overview of SEMs that focuses on the general SEM and the process involved in an SEM analysis. A typical SEM analysis unfolds in five steps. The first step involves model specification in which an analyst brings theory and substantive knowledge to decide on the structure of the model. The second step involves assessing whether the specified model is identified. Once a model is identified, the third step is to estimate the parameters using one of the several estimators available for SEMs. The fourth step includes examining the fit of the model, both overall and in components, and relative to alternative models if desired. In many cases, initial models turn out to have poor fit with the structure of the data and thus the fifth step concerns respecification or considering alternative models that may have better fit. This entry concludes with a brief discussion of three particularly notable extensions of the general SEM: the incorporation of categorical endogenous observed variables, the specification of categorical latent variables, and the use of SEMs with longitudinal data.

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