Comparison of Statistical Power for Testing Interactive Versus Quadratic Effects Using Measured Variable Versus Latent Variable Approaches

• Activity Number: 470
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Education
• Author(s): Yue Ma*+ and Leona Aiken and Stephen West
• Companies: University of South Florida and Arizona State University and Arizona State University
• Keywords: Statistical Power ; Structural Equation Modeling ; Latent Variable ; OLS Regression ; Interaction ; Quadratic

Abstract

The statistical power for detecting an interaction versus a quadratic effect using OLS regression for scale scores versus structural equation modeling (SEM) of latent variables was compared through simulation and analytic work. Models studied included two predictors and one nonlinear effect, either their interaction or a single quadratic term. OLS had greater power than SEM. OLS had attenuated parameter estimates, but smaller standard errors and MSEs relative to SEM for nonlinear terms. Comparisons equating the magnitude of the coefficients for the nonlinear terms showed greater power for the test of the quadratic term than the interaction term, which diminished as the interpredictor correlation increased. Comparisons equating the squared semi-partial correlations of the nonlinear terms showed equal power at low correlations, with the power for the interaction term exceeding that of the quadratic term as the interpredictor correlation increased. Results were interpreted in terms of (1) attenuation in parameter estimates for OLS, (2) negative bias in standard error estimates for SEM, and (3) differences between theoretical versus empirical standard errors for both OLS and SEM.