Detecting Nonlinearities in Structural Equation Modeling Using Residual Plots

• Activity Number: 257
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Graphics
• Author(s): Laura Hildreth*
• Companies: Montana State University
• Keywords: structural equation modeling ; residual analysis ; residual plots ; factor scores

Abstract

The validity of analyses using structural equation modeling (SEM) relies on several assumptions, analogous to those in regression analysis. One assumption is that of linearity, implying that all equations are linear in both the (observed and latent) variables and the parameters. Violating this assumption is detrimental as it may cause biased parameter and standard error estimates and misleading model diagnostics and test statistics. Though several methods have been developed to estimate nonlinear effects they assume that the nature of the relationship is known a priori. Few diagnostics have been developed to assess the linearity assumption or to explore the nature of a nonlinear relationship. The purpose of this paper is to examine the use of residual plots to identify nonlinearities in SEM. The utility of these plots is assessed using simulated data. Results indicate that residual plots are able to detect nonlinear relationships and thus are a viable graphical diagnostic tool to evaluate the linearity assumption in SEM but the utility of the plots depends on how the residuals are calculated.