On the use of the finite iterative method for computing the implied covariance matrix in structural equation models

Abstract

Structural Equation Modeling (SEM) is a widely used framework for analyzing relationships among observed and latent variables, with the estimation process representing a critical step. A central component of estimation is the computation of the implied covariance matrix. A key observation motivating this work is an implicit structural constraint arising from the equality between the empirical variances of the manifest variables and the diagonal of the implied covariance matrix. This constraint is not explicitly considered in the classical CB-SEM framework, which relies on Jöreskog’s formulation. An alternative approach based on the Finite Iterative Method (FIM) is proposed for constructing the implied covariance matrix. The proposed method naturally incorporates the variance constraint within its algorithmic structure, resulting in a substantial reduction in the number of free parameters by nearly half, thereby yielding a more parsimonious representation and reducing computational burden. The performance of the FIM-based approach is evaluated through empirical analysis and a simulation study, demonstrating its numerical stability, parsimony, and equivalence with classical SEM estimation.