Diagnostic plot for the Identification of high leverage collinearity-influential observations

• Arezoo Bagheri ^[2] ; Habshah Midi ^[1]
  1. [1] Universiti Putra Malaysia

     Universiti Putra Malaysia

     Malasia

     
  2. [2] National Population Studies and Comprehensive Management Institute
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 39, Nº. 1, 2015, págs. 51-70
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • High leverage collinearity influential observations are those high leverage points that change the multicollinearity pattern of a data. It is imperative to identify these points as they are responsible for misleading inferences on the fitting of a regression model. Moreover, identifying these observations may help statistics practitioners to solve the problem of multicollinearity, which is caused by high leverage points. A diagnostic plot is very useful for practitioners to quickly capture abnormalities in a data. In this paper, we propose new diagnostic plots to identify high leverage collinearity influential observations. The merit of our proposed diagnostic plots is confirmed by some well-known examples and Monte Carlo simulations.

• Referencias bibliográficas
  • Andersen, R. (2008). Modern Methods for Robust Regression. Sara Miller McCune: SAGE publications, USA.
  • Bagheri, A.,Habshah, M. and Imon, A. H. M. R. (2009). Two-step robust diagnostic method for identification of multiple high leverage points....
  • Bagheri, A., Habshah, M. and Imon, A. H. M.R. (2012). A novel collinearity-influentialobservation diagnostic measure based on a group deletion...
  • Bagheri, A., Habshah, M. (2009). Robust estimations as a remedy for multicollinearity caused by multiple high leverage points. Journal of...
  • Bagheri, A., Habshah, M. (2011). On the performance of robust variance inflation factors. International Journal of Agricultural and Statistics...
  • Bagheri, A., Habshah, M. (2012). On the performance of the measure for diagnosing multiple high leverage collinearity-reducing observations....
  • Belsley, D. A., Kuh, E. and Welsch, R. E. (1980). Regression Diagnostics: Identifying : Influential Data and Sources of Collinearity. Wiley,...
  • Belsley, D. A. (1991). Conditioning Diagnostics: Collinearity and Weak Data in Regression. Wiley, New York.
  • Cook, R. D. and Weisberg, S. (1982). Residuals and Influence in Regression. Chapman Hall, London.
  • Gray, J. B. (1983). The L-R plot: a graphical tool for assessing influence. Proceedings of the statistical computing section. American statistical...
  • Habshah, M. and Bagheri, A. (2013). Robust multicollinearity diagnostic measures based on minimum covariance determination approach. Economics...
  • Habshah, M., Norazan, M. R. and Imon, H. M. R. (2009). The performance of diagnostic-robust generalized potentials for the identification...
  • Habshah, M., Bagheri, A. and Imon, A. H. M. R. (2010). The application of robust multicollinearity diagnostic method based on robust coefficient...
  • Habshah, M., Bagheri, A. and Imon, A. H. M. R. (2011). High leverage collinearity-enhancing observation and its effect on multicollinearity...
  • Hadi, A. S. (1988). Diagnosing collineariy-influential observations. Computational Statistics and Data Analysis, 7, 143–159.
  • Hadi, A. S. (1992). A new measure of overall potential influence in linear regression. Computational Statistics and Data Analysis, 14, 1–27.
  • Hawkins, D. M., Bradu, D. and Kass, V. (1984). Location of several outliers in multiple regression data using elemental sets. Technometrics,...
  • Imon, A. H. M. R. (2002). Identifying multiple high leverage points in linear regression. Journal of Statistical Studies. Special Volume in...
  • Kamruzzaman, M. D. Imon, A. H. M. R. (2002). High leverage point: Another source of multicollinearity. Pakistan Journal of Statistics, 18,...
  • Kutner, M. H., Nachtsheim, C. J., Neter, J. and Li,W. (2005). Applied Linear RegressionModels 5th Edition. MacGraw-Hill,New York.
  • Lawrence, K. D. and Arthur, J. L. (1990). Robust Regression: Analysis and Applications. INC: Marcel Dekker.
  • Moller, S. F., Frese, J. V. and Bro, R. (2005). Robust methods for multivariate data analysis. Journal of Chemometrics, 19, 549–563.
  • Myers, R. H. (1990). Classical and Modern Regression with Applications. 2nd Edition. CA: Duxbury Press.
  • Rousseeuw, P. J. and Leroy, A. M. (1987). Robust Regression and Outlier Detection. New York: Wiley.
  • Rousseeuw, P. J. and Van Driessen, K.(1999). A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41, 212–223.
  • Rousseeuw, P. and Van Zomeren, B. (1990). Unmasking multivariate outliers and leverage points. Journal of American Statistical Association,...
  • Sall, J. (1990). Leverage plots for general linear hypothesis. The American Statistician, 44, 308–315.
  • Sengupta, D. and Bhimasankaram, P. (1997). On the roles of observations in collinearity in the linear model. Journal of American Statistical...
  • Stine, R. A. (1995). Graphical interpretation of variance inflation factors. The American Statistician, 49, 53–56.