K-Clustering as a Detection Tool for Influential Subsets in Regression

Abstract

This article describes a new methodology for the detection of influential subsets in regression. The method is based on an adaptation of computational and graphical techniques used in cluster analysis and makes use of some general properties of influential subsets, but it is independent of any specific measure of influence. For small to moderate data sets the proposed method is computationally efficient, compared to existing search methods, and it identifies subset candidates that merit attention according to some or all measures of joint influence that have appeared in the literature to date. Examples are given illustrating the method applied to two data sets previously analyzed in published studies.

KEY WORDS:

• Joint influence
• Regression diagnostics
• Cluster analysis
• Hat matrix
• Influential case
• Leverage