Optimizing Ridge Generalized Least Squares for Structural Equation Modeling

Abstract

Ridge generalized least squares (RGLS) is a recently proposed estimation procedure for structural equation modeling. In the formulation of RGLS, there is a key element, ridge tuning parameter, whose value determines the efficiency of parameter estimates. This article aims to optimize RGLS by developing formulas for the ridge tuning parameter to yield the most efficient parameter estimates in practice. For the formulas to have a wide scope of applicability, they are calibrated using empirical efficiency and via many conditions on population distribution, sample size, number of variables, and model structure. Results show that RGLS with the tuning parameter determined by the formulas can substantially improve the efficiency of parameter estimates over commonly used procedures with real data being typically nonnormally distributed.

Keywords:

• efficiency
• empirical modeling
• Monte Carlo simulation
• parameter estimation

Notes

¹ The values of both the relative multivariate skewness and the relative multivariate kurtosis are approximately 1.0 for normally distributed data.

² The convergence is defined as, within 300 iterations, the maximum difference for all elements of θ between two consecutive iterations is smaller than .0001.

³ The figure is created by an online interface for drawing path diagrams for SEM: http://semdiag.psychstat.org/.

Additional information

Funding

This research was supported by the National Science Foundation [SES-1461355].