A Critique of Some Ridge Regression Methods: Rejoinder.

The papers is concerned primarily with two fundamental issues. The use of multicollinearity measures to determine if the data are sufficiently weak to justify ridge regression, and the selection of a normalization or particular linear transformation to which ridge regression is applied. There are several specific points that the researchers will try to clarify. It is far from certain what measure of data strength is most appropriate for a choice between least squares and ridge regression. Many authors focus on the mean squared errors of the parameter estimates, but there is still the problem of deciding which parameters should receive the most attention. One scalar answer that appeals to these statisticians is mean squared prediction error using the out-of sample values of the variables for which the model will be employed. Those researchers whose objectives cannot be put in a forecasting context may want to look elsewhere for evidence of unsatisfactory estimates. Multicollinearity can cause or explain imprecise estimates but, since it is not the only cause or explanation, measures of multicollinearity are an inadequate gauge of precision. The same cautions that apply to variance inflation factors also apply to Thisted's multicollinearity indexes.