Local influence diagnostics with forward search in regression analysis

Regression analysis is one of the most widely used statistical techniques. It is well known that the least squares estimates is sensitive to atypical and/or influential observations. Many methodologies were proposed to detect influential observations considering case deletion (global influence). On the other hand, Cook (J R Stat Soc Ser B 48(2):133–169, 1986) developed a general and powerful methodology to obtain a group of observations that might be jointly influential considering the local influence. However, these techniques may fail to detect masked influential observations. In this paper, we propose a methodology to detect masked influential observations in a local influence framework considering the forward search (Atkinson and Riani, Robust diagnostic regression analysis, Springer, New York, 2000). The usefulness of the proposed methodology is illustrated with data sets which were previously analyzed in the literature to detect outliers and/or influential observations. Masked influential observations were successfully identified in these studies. The proposed methodology may be used in any model where the local influence analysis (Cook 1986) is appropriate.