Leverage, residual, and interaction diagnostics for subsets of cases in least squares regression

Leverage and residual Values are useful general diagnostics in least squares regression because all single-case influence measures are functions of these two basic components. Recent work in the area of robust diagnostics has suggested that ordinary leverage and residual Values can be ineffective in the presence of ''masking'' and other multiple case effects, but Kempthorne and Mendel (1990) and others have pointed out that satisfactory definitions of ''leverage'' and ''residual'' for subsets of cases might overcome these problems. In this article, we propose a set of three simple, yet general and comprehensive, subset diagnostics (referred to as leverage, residual, and interaction) that have the desirable characteristics of single-case leverage and residual diagnostics. Most importantly, the proposed measures are the basis of several existing subset influence measures, including Cook's distance. We illustrate how these basic diagnostics usefully complement existing multiple outlier detection procedures and subset influence measures in understanding the influence structure within a regression data set. (C) 1997 Elsevier Science B.V.