The Identification of Influential Groups in Linear Regression Models via an Influence Matrix Approach

The Cook's distance measure is a prominent diagnostic tool for influence measure in linear regression diagnostics. Many authors have studied it, and the main focus is on its use for detection of a single influential observation in linear regression. In this work, we propose a standardized version of it and extend the single-case form to flag influential subsets. The proposed method uses diagonal and off-diagonal elements of a normalized influence matrix <img src=image/13441459_01.gif>. The main diagonal elements of <img src=image/13441459_01.gif> consist of the standardized univariate Cook statistics, and the off-diagonal elements consist of useful statistics that can detect influential subsets. A scattergram of the off-diagonal components of <img src=image/13441459_01.gif> is drawn, and bounds (lower and upper bounds) are imposed on it. These bounds form the main artillery for detecting influential subsets. One of the glaring advantages of the approach is that it facilitates the identification of influential subsets that would be lost if only the main diagonal entries of <img src=image/13441459_01.gif> are explored. The method is effective and computationally simple to apply, especially where more complex methods are not easy to implement, because they are computationally intensive. Analysis of well-known real-life data sets in linear regression diagnostics is used to illustrate the application and usefulness of the proposed method.