| When attempting to predict a criterion from a set of highly inter-related or multicollinear predictors the estimates of the optimal predictor weights or regression coefficients are unstable. Proponents of a new technique, ridge regression, have found that it can reduce the total mean squared error of the conventional ordinary least squares (OLS) regression coefficients under conditions of predictor multicollinearity. The published studies comparing ridge and least squares regression are, however, limited by confounding the effects of multicollinearity and the values of the true regression coefficients in a way that favored ridge. As a result, these studies do not provide a basis for determining when or when not to use ridge in place of OLS regression.;The present study investigates ridge and OLS estimates of the true regression coefficients under conditions chosen to eliminate this confounding. From large scale simulations it was found that, contrary to some previous work, ridge regression in general was not a solution to the problem of coefficient instability due to multicollinearity. Ridge regression was found to enhance estimational accuracy only if the true coefficients declined in importance with the eigenvalues of the predictor matrix. If, however, the true coefficients remained equal or increased as the eigenvalues decreased, ridge regression often performed substantially worse than OLS. By far the greatest determinant of the success or failure of ridge regression was this orientation of the true coefficients with respect to the eigenvalues. Even without multicollinearity, if the coefficients declined with the eigenvalues, ridge offered some improvement over OLS. The present study demonstrates that ridge does not solve the problems of multicollinearity except under a specific orientation of the true coefficients. However, since the true coefficients are ordinarily not known, this study shows that routine use of ridge regression involves substantial risk of less accurate performance than OLS. |
