Collinearity: revisiting the variance inflation factor in ridge regression

References

• J.E. Anderson, Ridge regression of house value determinants, J. Urban Econ. 9 (1981), pp. 286–297. doi: 10.1016/0094-1190(81)90028-0
   Web of Science ®Google Scholar
• B. Bruce and D.W. Hann, Applications of ridge regression in forestry, Forest Sci. 27 (1981), pp. 339–348.
   Web of Science ®Google Scholar
• S. Das and S. Chatterjee, Multicollinearity problem root cause diagnostic and way out, Soc. Sci. Res. Netw. (2011); available at http://ssrn.com/abstract=1830043.
   Google Scholar
• J. Dias and J. Castro, New multicollinearity indicators in linear regression models, Int. Statist. Rev. 75 (2007), pp. 114–121. doi: 10.1111/j.1751-5823.2007.00007.x
   Web of Science ®Google Scholar
• J. Dias and J. Castro, The corrected vif, J. Appl. Stat. 38 (2011), pp. 1499–1507. doi: 10.1080/02664763.2010.505956
   Web of Science ®Google Scholar
• L. Feng-Jeng, Solving multicollinearity in the process of fitting regression model using the nested estimate procedure, Qual. Quant. 42 (2008), pp. 417–426. doi: 10.1007/s11135-006-9055-1
   Web of Science ®Google Scholar
• J. Fox, Applied Regression Analysis, Linear Models, and Related Methods, Sage, Thousand Oaks, CA, 1997.
   Google Scholar
• J. Fox and G. Monette, Generalized collinearity diagnostics, J. Amer. Statist. Assoc. 87 (1992), pp. 178–183. doi: 10.1080/01621459.1992.10475190
   Web of Science ®Google Scholar
• C.B. García, J. García and J. Soto, The raise method: An alternative procedure to estimate the parameters in presence of collinearity, Qual. Quant. 45 (2010), pp. 403–423. doi: 10.1007/s11135-009-9305-0
   Web of Science ®Google Scholar
• R. Garg, Ridge regression in the presence of multicollinearity, Psychol. Rep. 54 (1984), pp. 559–566. doi: 10.2466/pr0.1984.54.2.559
   Web of Science ®Google Scholar
• W.H. Greene, Econometric Analysis, 2nd ed., Prentice-Hall, New Jersey, 1993.
   Google Scholar
• A.S. Hadi, Ridge and surrogate ridge regressions, in International Encyclopedia of Statistical Science, Springer, New York, 2011.
   Google Scholar
• J.F. Hair, R.E. Anderson, R.L. Tatham and W.C. Black, Multivariate Data Analysis with Readings, 4th ed., Prentice-Hall, New Jersey, 1995.
   Google Scholar
• A.E. Hoerl, Application of ridge analysis to regression problems, Chem. Eng. Progress 58 (1962), pp. 215–223.
   Google Scholar
• A.E. Hoerl, Ridge analysis, Chem. Eng. Progress 60 (1964), pp. 67–77.
   Google Scholar
• A.E. Hoerl and R.W. Kennard, Ridge regression: Applications to nonorthogonal problems, Technometrics 12 (1970), pp. 69–82. doi: 10.1080/00401706.1970.10488635
   Web of Science ®Google Scholar
• A.E. Hoerl and R.W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems, Technometrics 12 (1970), pp. 55–67. doi: 10.1080/00401706.1970.10488634
   Web of Science ®Google Scholar
• M.A. Ijomah and M.T. Nwakuya, Ridge trace a boost to ridge regression estimate in the presence of multicollinearity, Sci. Afr. 10 (2011), pp. 42–47.
   Google Scholar
• M. Irfan, M. Javed and M. Ali Raza, Comparison of shrinkage regression methods for remedy of multicollinearity problem, Middle East J. Sci. Res. 14 (2013), pp. 570–579.
   Google Scholar
• N. Jamal and M.Q. Rind, Ridge regression: A tool to forecast wheat area and production, Pak. J. Statist. Oper. Res. 3 (2007), pp. 125–134.
   Google Scholar
• D.R. Jensen and D.E. Ramirez, Anomalies in the foundations of ridge regression, Int. Statist. Rev. 76 (2008), pp. 89–105. doi: 10.1111/j.1751-5823.2007.00041.x
   Web of Science ®Google Scholar
• D.R. Jensen and D.E. Ramirez, Surrogate models in ill-conditioned systems, J. Statist. Plan. Inference 140 (2010), pp. 2069–2077. doi: 10.1016/j.jspi.2010.02.001
   Web of Science ®Google Scholar
• D.R. Jensen and D.E. Ramirez, Tracking MSE efficiencies in ridge regression, Adv. Appl. Statist. Sci. 1 (2010), pp. 381–398.
   Google Scholar
• D.R. Jensen and D.E. Ramirez, Revision: Variance inflation in regression, Adv. Decis. Sci. 2013 (2013), pp. 1–15. doi: 10.1155/2013/671204
   Google Scholar
• P.A. Kennedy, A Guide to Econometrics, 3rd ed., MIT Press, Cambridge, MA, 1992.
   Google Scholar
• E.R. Mansfield and P. Billy, Detecting multicollinearity, Amer. Statist. 36 (1982), pp. 158–160.
   Web of Science ®Google Scholar
• S. Mardikyan and E. Cetin, Efficient choice of biasing constant for ridge regression, Int. J. Contemp. Math. Sci. 3 (2008), pp. 527–536.
   Google Scholar
• C. Marinoiu, A ridge regression models for the cracking process, Buletinul Universitati Petrol Gaze din Ploiesti. LXI (2009), pp. 65–70.
   Google Scholar
• D.W. Marquardt, Generalized inverses, ridge regression, biased linear estimation and nonlinear estimation, Technometrics 12 (1970), pp. 591–612. doi: 10.2307/1267205
   Web of Science ®Google Scholar
• D.W. Marquardt and S.R. Snee, Ridge regression in practice, Amer. Statist. 29 (1975), pp. 3–20.
   Web of Science ®Google Scholar
• R.L. Mason, R.F. Gunst and J.L. Hess, Statistical Design and Analysis of Experiments: Applications to Engineering and Sciences, Wiley, New York, 1989.
   Google Scholar
• G.C. McDonald, Tracing ridge regression coefficients, Wiley Interdiscip. Rev.: Comput. Statist. 2 (2010), pp. 695–703. doi: 10.1002/wics.126
   Google Scholar
• G.C. McDonald and R.C. Schwing, Instabilities of regression estimates relating air pollution to mortality, Technometrics 15 (1973), pp. 463–481. doi: 10.1080/00401706.1973.10489073
   Web of Science ®Google Scholar
• S. Menard, Applied Logistic Regression Analysis: Sage University Series on Quantitative Applications in the Social Sciences, Sage, Thousand Oaks, CA, 1995.
   Google Scholar
• J. Neter, W. Wasserman and M.H. Kutner, Applied Linear Regression Models, 2nd ed., Irwin, Homewood, IL, 1989.
   Google Scholar
• R.M. O'Brien, A caution regarding rules of thumb for variance inflation factors, Qual. Quant. 41 (2007), pp. 673–690. doi: 10.1007/s11135-006-9018-6
   Web of Science ®Google Scholar
• B. Price, Ridge regression: Application to nonexperimental data, Psychol. Bull. 84 (1977), pp. 759–766. doi: 10.1037/0033-2909.84.4.759
   Web of Science ®Google Scholar
• H. Theil, Principles of Econometrics, Wiley, New York, 1971.
   Google Scholar
• H.J.P. Timmermans, Multiattribute shopping models and ridge regression analysis, Environ. Plann. A 13 (1981), pp. 43–56. doi: 10.1068/a130043
   Web of Science ®Google Scholar
• W.A. Williams, C.O. Qualset and S. Geng, Ridge regression for extracting soybean yield factors, Crop Sci. 19 (1979), pp. 869–873. doi: 10.2135/cropsci1979.0011183X001900060030x
   Web of Science ®Google Scholar
• J. Zhang and M. Ibrahim, A simulation study on spss ridge regression and ordinary least squares regression procedures for multicollinearity data, J. Appl. Stat. 32 (2005), pp. 571–588. doi: 10.1080/02664760500078946
   Web of Science ®Google Scholar