When a theory aims to explain associations among latent variables, a structural model can be added to the measurement model to produce a full SEM. The structural model of a SEM relates latent variables to each other via directed regression coefficients. It can be written in matrix notation as η=Bη+ζ, where B is an m × m matrix of regression coefficients that relate latent variables to each other and ζ is an m × 1 vector of latent variable residuals. The model implied covariance matrix of observed variables is Σ(θ)=Λ(I-B)−1 Ψ(I-B′)−1 Λ′+Θ, where I is an k × k identity matrix.41 Thus, in a full SEM, the empirical matrix is represented by a set of parameters that relate observed variables to latent variables, and relate latent variables to each other in a series of linear equations.
