Alternative Estimation Methods

Notice that this is a much simpler function (e.g., no logs), and it is clear that the discrepancy between the obtained covariance matrix and the covariance matrix implied by the model (S-Σ) is minimized after weighting it by W. Although any W can be chosen for the weight matrix, most commonly, the inverse of the covariance matrix, S, is used in SEM packages. FGLS is asymptotically equivalent to FML, meaning that as sample sizes increase, they are approximately equal. FGLS is based on the same assumptions as FML and would be used under the same conditions. It is thought to perform less well, however, in small samples, so FML is usually chosen instead of FGLS. The simplicity of the function, however, means that other weight matrices could be used in an attempt to correct for violations of distributional assumptions.