465 – Graphics Potluck

Residual Plots to Identify Outliers Structural Equation Modeling

at Iowa State University

Residual plots are routinely used in regression analysis to evaluate underlying model assumptions and identify potential outliers. Similar graphical tools are considerably more difficult to construct under the framework of structural equation modeling (SEM) as the use of latent variables complicates the construction of such residual-based diagnostics. The purpose of this paper is to introduce a method to construct residual plots under the SEM framework. First we present a class of residual estimators that are weighted linear functions of the observed variables. We then propose a method to construct residual plots under the SEM framework analogous to ``residuals versus fitted values plots' in regression analysis. The utility of these plots to identify potential outliers is demonstrated by implementing our method using Mardia's exam data. This example illustrates that the choice of residual estimator affects the residual plots and provides insight into which residual estimator is the ``best.' Compared to previous diagnostics to identify outliers in SEM, we develop a graphical diagnostic that not only provides a more consistent method of identifying outliers but also identifies why an observation is outlying. Ultimately, this work provides the foundation for the use of residual plots and future development of residual analysis in SEM.