This article explains the use of factor analysis types of models to develop measures of latent concepts which were then combined with causal models of the underlying latent concepts. In particular, it offers an overview of the classic structural equation models (SEMs) when the latent and observed variables are continuous. Then it looks at more recent developments that include categorical, count, and other noncontinuous variables as well as multilevel structural equation models. The model specification, assumptions, and notation are covered. This is followed by addressing implied moments, identification, estimation, model fit, and respecification. The penetration of SEMs has been high in disciplines such as sociology, psychology, educational testing, and marketing, but lower in economics and political science despite the large potential number of applications. Today, SEMs have begun to enter the statistical literature and to re-enter biostatistics, though often under the name ‘latent variable models’ or ‘graphical models’.
Model Fit Estimation for Multilevel Structural Equation Models