Influence Measures in Ridge Regression

In regression, it is of interest to detect anomalous observations that exert an unduly large influence on the least squares analysis. Frequently, the existence of influential data is complicated by the presence of collinearity (see, e.g., Lawrence and Marsh 1984). Very little work has been done, however, on the possible effects that collinearity can have on the influence of an observation. In this article, we show that when ridge regression is used to mitigate the effects of collinearity, the influence of some observations can be drastically modifield. Approximate deletion formulas for the detection of influential points are proposed for ridge regression.