Offending Estimates in Covariance Structure Analysis: Comments on the Causes of and Solutions to Heywood Cases

In this article we discuss, illustrate, and compare the relative efficacy of three recommended approaches for handling negative error variance estimates (i.e., Heywood cases): (a) setting the offending estimate to zero, (b) adopting a model parameterization that ensures positive error variance estimates, and (c) using models with equality constraints that ensure nonnegative (but possibly zero) error variance estimates. The three approaches are evaluated in two distinct situations: Heywood cases caused by lack of fit and misspecification error, and Heywood cases induced from sampling fluctuations. The results indicate that in the case of sampling fluctuations the simple approach of setting the offending estimate to zero works reasonably well. In the case of lack of fit and misspecification error, the theoretical difficulties that give rise to negative error variance estimates have no ready-made methodological solutions.