Ridge Structural Equation Modeling with Correlation Matrices for Ordinal and Continuous Data

• Activity Number: 288
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Ke-Hai Yuan*+ and Ruilin Wu and Peter M. Bentler
• Companies: University of Notre Dame and Beihang University and University of California, Los Angeles
• Keywords: Polychoric correlation ; bias ; efficiency ; convergence ; mean square error ; overall model evaluation

Abstract

This paper develops a ridge procedure for structural equation modeling (SEM) with ordinal and continuous data by modeling polychoric/polyserial/product-moment correlation matrix R. Rather than directly fitting R, the procedure fits a structural model to R_a=R+aI by minimizing the normal-distribution-based discrepancy function, where a>0. Statistical properties of the parameter estimates are obtained. Four statistics for overall model evaluation are proposed. Empirical results indicate that the ridge procedure for SEM with ordinal data has better convergence rate, smaller bias, smaller mean square error and better overall model evaluation than the widely used maximum likelihood procedure.