Net Effect Plots for Non-Elliptically Distributed Predictors

• Activity Number: 310
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Graphics
• Author(s): Xin Zhang*+ and R. Dennis Cook
• Companies: University of Minnesota at Twin Cities and University of Minnesota
• Keywords: Net Effect Plots ; Sufficient Dimension Reduction ; Central Solution Subspaces

Abstract

The net effect plot (Cook 1995) is a very useful tool for studying the contribution of selected predictors to a regression problem, with or without a pre-specified parametric model. We focus on graphical methods for studying the contribution of a subset of predictors after fully accounting for the contributions of the rest of predictors to the regression. While marginal plots might be misleading and added variable plots usually overestimate the importance of the selected predictors, net effect plots can reveal their true contribution. At the same time, sufficient dimension reduction in regression is a useful precursor that can facilitate the study. Specifically, using dimension reduction methods to find a sufficient distributional index function (Cook 1995) makes brushing, linking and analyzing net effect plots much easier. In particular, the methods based on Central Solution Subspaces (Li and Dong 2009) could be used even when the predictors are non-elliptically distributed.

References: Cook, R. D. (1995). Graphics for studying the net e?ects of regression predictors. Li, B. and Dong, Y. (2009). Dimension Reduction for Nonelliptically distributed predictors.