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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 531607, 16 pages
http://dx.doi.org/10.1155/2012/531607
Research Article

On the Performance of the Measure for Diagnosing Multiple High Leverage Collinearity-Reducing Observations

1Laboratory of Computational Statistics and Operations Research, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 2 August 2012; Revised 9 December 2012; Accepted 9 December 2012

Academic Editor: Stefano Lenci

Copyright © 2012 Arezoo Bagheri and Habshah Midi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

There is strong evidence indicating that the existing measures which are designed to detect a single high leverage collinearity-reducing observation are not effective in the presence of multiple high leverage collinearity-reducing observations. In this paper, we propose a cutoff point for a newly developed high leverage collinearity-influential measure and two existing measures ( and ) to identify high leverage collinearity-reducing observations, the high leverage points which hide multicollinearity in a data set. It is important to detect these observations as they are responsible for the misleading inferences about the fitting of the regression model. The merit of our proposed measure and cutoff point in detecting high leverage collinearity-reducing observations is investigated by using engineering data and Monte Carlo simulations.