Treatment of Correlated Errors in Structural Equation Models

Structural Equation Models allow assessing the conformity of a theoretical model to some given data. The fundamental hypothesis of the covariance-based approach is that the covariance matrix of the model variables can be generated by the model. This matrix is called the implied covariance matrix. Several methods are used for its computation. However, it depends on many assumptions that may sometimes be unrealistic. In this paper, we assess the assumption of the correlation of the error terms and we proposed a correction to the iterative method for the computation of the implied covariance matrix. Theoretical, as well as numerical illustrations, are given to show the advantage of the corrected method.