The hypothesized structural relations between latent variables are defined by a set of equations in a SEM model. Different from the path analysis, SEM focuses causal relationships among unobserved latent variables instead of among observed variables. Recall that a SEM model is a two-part model, consisting of the measurement model (CFA) and structural equations. In the measurement model part of the model, linear (e.g., when observed indicators are continuous measures) or nonlinear (e.g., when observed indicators are categorical measures) equations describe the relations between the observed variables and their underlying latent variables/factors; and in the structural equations part of the model, endogenous latent variables () are regressed on the exogenous latent variables () and/or some other endogenous latent variables. In addition, observed variables can also be included as either dependent and/or independent variables in a SEM model.
The measurement model part of the SEM model is described as:
where and are vectors of intercepts of regressing ...