An Empirical Study of Polychoirc Instrumental Variable Estimation in Structural Equation Models

• Activity Number: 181
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Shaobo Jin*+ and Hao Luo and Fan Yang-Wallentin
• Companies: Uppsala University and University of Hong Kong and Uppsala University
• Keywords: ordinal data ; polychoric correlation ; instrumental variable ; unweighted least squares ; diagonally weighted least squares ; maximum likelihood

Abstract

Traditional methods to fit a structural equation model (SEM) utilize the entire model specification in estimation. In this paper, we conduct a simulation study to compare the equation-by-equation estimation method polychoric instrumental variable (PIV) estimation with the full information methods such as unweighted least squares (ULS), diagonally weighted least squares (DWLS) and maximum likelihood (ML). 81 settings are considered, which are (a) two models (factor model and SEM), (b) three sample sizes (400, 800, and 3200), (c) three distributions (normal, moderately, and extremely non-normal), (d) one level of number of categories (5 categories), (e) three levels of misspecification for the factor model and four levels of misspecification for the SEM. Simulation results show that the PIV estimators are competitive alternatives of the ULS, DWLS, and ML estimators for the CFA model. However, PIV estimators are not suitable for the complex SEM models with high bias and percentages of improper solutions.