Observational Residuals in Factor Analysis and Structural Equation Models

In the last decade there has been a surge of interest in the role of outliers and residuals in statistical analyses. However, there is a surprising neglect of these topics in factor analysis and in other structural equation models with latent variables. In this paper we propose ways to calculate unstandardized residuals, derive standardized residuals, suggest tests of statistical significance for residuals, and illustrate the procedures with empirical and simulated data. Our significance tests for the residuals are based on asymptotic theory, but our examples indicate that the tests are helpful even with N's of 60 to 100.