Deletion Influence and Masking in Regression

SUMMARY The paper is concerned with masking of Cook's distance, the popular deletion measure of influence of individual data cases in linear regression. Masking is broadly concerned with the limitations imposed by the use of individual cases. Two specific views are drawn from quotations: the first is associated with the established idea of joint influence, i.e. the deletion of two or more cases simultaneously, and the second is conditional influence, i.e. the calculation of Cook's distance before and after the deletion of other cases. Attention is mainly focused on pairs of already identified cases. Intuitive understanding is obtained via explicit general forms for joint and conditional Cook's distance influence with pairs of cases; especially tractable results are obtained for replicate and opposite explanatory pairs, and for multiples of individual cases of opposite pairs. The noteworthy effects possible in joint influence are described as reducing, enhancing and swamping; in conditional influence, interesting effects are described as masking and boosting. Thus only in connection with one effect in conditional influence is the term masking used. The work is illustrated on one constructed and one reported data set.