Outliers and Improper Solutions

Abstract

A common occurrence in structural equation models are “improper solutions.” Estimates of negative variances of measurement errors, negative variances of equation errors, or correlations between latent variables that are greater than one are instances of improper solutions. Recent work has begun to examine the causes and cures for these problems but the role of outliers in generating improper solutions has been overlooked. The purposes of this article are threefold: (1) to explain how outliers can lead to improper solutions, (2) to use a confirmatory factor analysis example to demonstrate this, and (3) to encourage researchers to check for this possibility.