Optimizing Ridge Generalized Least Squares for Structural Equation Modeling

Ridge generalized least squares (RGLS) is a recently proposed estimation procedure for structural equation modeling (SEM). The weight matrix for RGLS is obtained by combining the sample fourth-order moment matrix with the identity matrix, and the relative contribution of each matrix is determined by a ridge tuning parameter. Empirical results showed that, with nonnormally distributed data, parameter estimates by RGLS can be much more accurate than those by the traditional methods. However, test statistics following RGLS are still unable to control type I errors well, especially when the sample size is small. This dissertation proposes to optimize the RGLS procedure in three directions. First, formulas are developed for the ridge tuning parameter to yield the most efficient parameter estimates in practice. Second, corrections are developed for the test statistics following RGLS to yield well-controlled type I errors. Third, corrected formulas are developed for the standard errors of RGLS estimates to be more accurate. For the formulas and corrections to have a wide scope of applicability, they are calibrated using Monte Carlo simulation with many conditions on population distribution, sample size, number of variables and model structure. The validity of the formulas and corrections are examined via an independent simulation study.