Efficient Computation of Subset Influence in Regression

Abstract The detection of influential cases is now accepted as an essential component of regression diagnostics. It is also well established that two or more cases that are individually regarded as noninfluential may act in concert to achieve a high level of joint influence. However, for the majority of data sets it is computationally infeasible to calculate the influence for all subsets of a given size. In this article we address this problem and suggest an algorithm that greatly reduces the computational effort by making use of a sequence of upper bounds on the influence value. These upper bounds are much less costly to evaluate and greatly reduce the number of subsets for which the influence value must be explicitly determined.