Estimator Conditioning Diagnostics for Covariance Structure Models

This article studies the utility of a general set of diagnostics based on extensions of the condition index and variance decomposition proportions advanced by Belsley and are useful for gauging the sensitivity of parameter estimates to conditioning problems arising from collinearity in the raw data.

Abstract

This article studies the utility of a general set of diagnostics for assessing conditioning problems in the covariance structure modeling framework. The diagnostics are based on extensions of the condition index and variance decomposition proportions advanced by Belsley and are based on using the covariance matrix of the estimates. A series of simulations with a variety of covariance structure models as well as a real data example show that these diagnostics are useful for gauging the sensitivity of parameter estimates to conditioning problems arising from collinearity in the raw data. The relationship between ill-conditioning and local identification as it pertains to the proposed diagnostics is also discussed. It is suggested that these diagnostics be implemented in existing covariance structure modeling software.