Structural Equation Modeling

Structural equation modeling (SEM) is a general term that describes a large number of statistical models used to evaluate the consistency of substantive theories with empirical data. It represents an extension of general linear modeling procedures such as analysis of variance and multiple regression. In addition, SEM can be used to study the relationships among latent constructs that are indicated by multiple measures and is applicable to experimental or nonexperimental data and to cross-sectional or longitudinal data.

SEM has a number of synonyms or special cases in the literature, including path analysis, causal modeling, and covariance structure analysis, or some variations of these terms. Path analysis is an extension of multiple regression in that various multiple regression models or equations can be estimated simultaneously; it provides a more effective and direct way of modeling mediation effects. Path analysis can be considered an early form and a special case of SEM in which structural relations among only observed variables are modeled. Structural relations are hypotheses about how independent variables affect dependent variables. Hence, the earlier path analysis or the later SEM is sometimes referred to as causal modeling. Because analyzing interrelations among variables is a major part of SEM and these interrelations are supposed to generate the observed covariance or correlation patterns among the variables, SEM is also sometimes called covariance structure analysis.

The measurement of latent variables originated from psychometric theories. Unobserved latent variables cannot be measured directly but are indicated or inferred by responses to a number of observable variables (indicators). Latent constructs such as intelligence or reading ability are often gauged by responses to a battery of items that are designed to tap those constructs. Responses of a participant are supposed to reflect where the participant stands on the scale of the latent variable. Factor analyses have been widely used to examine the number of latent constructs underlying the observed responses and to evaluate the adequacy of individual items or variables as indicators for the latent constructs they are supposed to measure. The mergence of confirmatory factor analysis models (sometimes called measurement models) with structural path models on the latent constructs became a general SEM framework in analyzing covariance structures. Today's advancement of SEM includes the modeling of mean structures in addition to covariance structures, the modeling of growth or changes over time (growth models), and the modeling of data having nesting structures (e.g., students are nested within classes, which in turn are nested within schools; multilevel models).