Collinearity, Ridge Regression, and Investigator Judgment

Abstract

Several recent articles have suggested that ridge regression may provide an "optimal" procedure for dealing with the problems created by highly collinear regressors in linear models. In this article, we review the consequences of collinearity among the regressors in a well-specified structural equation model and the several variants of ridge regression that may be considered as possible responses to such collinearity. Based on thts review and on application of several ridge regression methods to an actual structural equation model in which collinearity is high, it becomes clear that one or another form of investigator judgment is unavoidable when any specific estimates are obtained via a ridge adjustment. The article indicates how the several ridge techniques implicitly involve distinct criteria whereby an estimator should be judged and some of the complications involved in each.