- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 531607, 16 pages
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.
- D. C. Montgomery, E. A. Peck, and G. G. Viving, Introduction to Linear Regression Analysis, John Wiley & Sons, New York, NY, USA, 3rd edition, 2001.
- Md. Kamruzzaman and A. H. M. R. Imon, “High leverage point: another source of multicollinearity,” Pakistan Journal of Statistics, vol. 18, no. 3, pp. 435–447, 2002.
- M. H. Kutner, C. J. Nachtsheim, and J. Neter, Applied Linear Regression Models, McGraw-Hill, New York, NY, USA, 2004.
- S. Chatterjee and A. S. Hadi, Regression Analysis by Examples, John Wiley & Sons, New York, NY, USA, 4th edition, 2006.
- A. S. Hadi, “Diagnosing collinearity-influential observations,” Computational Statistics & Data Analysis, vol. 7, no. 2, pp. 143–159, 1989.
- M, A. Habshah, Bagheri, A. H. M. R, and Imon, “The application of robust multicollinearity diagnostic method based on robust coefficient determination to a non-collinear data,” Journal of Applied Sciences, vol. 10, no. 8, pp. 611–619, 2010.
- M. Habshah, A. Bagheri, and A. H. M. R. Imon, “High leverage collinearity-enhancing observations and its effect on multicollinearity pattern; Monte Carlo simulation study,” Sains Malaysiana, vol. 40, no. 12, pp. 1437–1447, 2011.
- A. Bagheri, H. Midi, and A. H. M. R. Imon, “The effect of collinearity-influential observations on collinear data set: A monte carlo simulation study,” Journal of Applied Sciences, vol. 10, no. 18, pp. 2086–2093, 2010.
- A. Bagheri and H. Midi, “On the performance of robust variance inflation factors,” International Journal of Agricultural and Statistical Sciences, vol. 7, no. 1, pp. 31–45, 2011.
- A. Bagheri, M. Habshah, and R. H. M. R. Imon, “A novel collinearity-influential observation diagnostic measure based on a group deletion approach,” Communications in Statistics, vol. 41, no. 8, pp. 1379–1396, 2012.
- M. Habshah, M. R. Norazan, and A. H. M. R. Imon, “The performance of diagnostic-robust generalized potentials for the identification of multiple high leverage points in linear regression,” Journal of Applied Statistics, vol. 36, no. 5-6, pp. 507–520, 2009.
- D. Sengupta and P. Bhimasankaram, “On the roles of observations in collinearity in the linear model,” Journal of the American Statistical Association, vol. 92, no. 439, pp. 1024–1032, 1997.
- A. S. Hadi, “A new measure of overall potential influence in linear regression,” Computational Statistics and Data Analysis, vol. 14, no. 1, pp. 1–27, 1992.
- A. H. M. R. Imon, “Identifying multiple high leverage points in linear regression,” Journal of Statistical Studies, vol. 3, pp. 207–218, 2002, Special Volume in Honour of Professor Mir Masoom Ali.
- D. A. Belsley, E. Kuh, and R. E. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, John Wiley & Sons, New York, NY, USA, 1980.
- D. A. Belsley, Conditioning Diagnostics-Collinearity and Weak Data in Regression, John Wiley & Sons, New York, NY, USA, 1991.
- D. C. Hoaglin and R. E. Welsch, “The Hat Matrix in regression and ANOVA,” Journal of the American Statistical Association, vol. 32, no. 1, pp. 17–22, 1978.
- P. Rousseeuw, “Multivariate estimation with high breakdown point,” in Mathematical Statistics and Applications, pp. 283–297, Reidel, Dordrecht, The Netherlands, 1985.
- D. C. Montgomery, G. C. Runger, and N. F. Hubele, Engineering Statistics, John Wiley & Sons, New York, NY, USA, 5nd edition, 2011.
- G. W. Stewart, “Collinearity and least squares regression,” Statistical Science, vol. 2, no. 1, pp. 68–100, 1987.
- K. D. Lawrence and J. L. Arthur, Robust Regression; Analysis and Applications, Marcel Dekker, New York, NY, USA, 1990.