Assessing global influential observations in modified ridge regression

Abstract

We occasionally find that a small subset of the data exerts a disproportionate influence on the fitted regression model. Theist, parameter estimates or predictions may depend more on the influential subset than on the majority of the data. We would like to locate these influential points and assess their impact on the model. If these influential points are bad values then they should be eliminated. On the other hand, there may be nothing wrong with these points, but if they control key model properties, as we would like for them to, they could affect the use of the model. When modified ridge regression (MRR) is used to mitigate the effects of multicollinearity, the influence of observations can be drastically modified. In this paper, we propose a case deletion formula to detect influential points in MRR. The [Longley, J.W., 1967. An appraisal of least squares programs for electronic computers from the point of view of the user. Journal of American Statistical Association 62,819–841] data is used to illustrate our methodology.