The default estimation methods that are used in the Structural Equation Models platform depend on the presence or absence of missing data. The Structural Equation Models platform uses maximum likelihood (ML) estimation by default when there are no missing data. If any missing data are detected, then the platform uses full information maximum likelihood (FIML) estimation by default. In both cases, standard errors are obtained using the observed information matrix. Robust maximum likelihood standard errors can be obtained using the Inference > Robust Inference option in the Structural Equation Models red triangle menu. When the Robust Inference option is used, a sandwich correction is applied to the standard errors to correct for a lack of efficiency in the presence of nonnormal data. The bread of the sandwich is the observed information matrix from the user-specified model, and the meat of the sandwich is the sum of the outer product of the gradient of the individual observations. The platform uses a combination of optimization algorithms in the estimation process, including Newton-Raphson, Quasi-Newton, and Fisher scoring.
Note: The ML method in the Structural Equation Models platform uses the sample size N in estimation, rather than N - 1.