Comparison of regression models under multi-collinearity


Multicollinearity is a major problem in linear regression analysis and several methods exists in the literature to deal with the same. Ridge regression is one of the most popular methods to overcome the problem followed by Generalized Ridge Regression (GRR) and Directed Ridge Regression (DRR). However, there exist many computational issues in using the above methods. Partial Ridge Regression (PRR) method is a computationally viable approach by selectively adjusting the ridge constants using the cutoff criteria. In this paper, the performance of the Partial Ridge Regression approach has been evaluated through a simulation study based on the mean squared error (MSE) criterion. Comparing with other methods of ridge regression, the study indicates that the Partial ridge regression by cutoff criteria performs better than the existing methods.

DOI Code: 10.1285/i20705948v11n1p340


Hoerl, A. E., & Kennard, R. W. (2000). Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 42(1), 80-86.

Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: applications to nonorthogonal problems. Technometrics, 12(1), 69-82.

Brownlee, K. A. (1965). Statistical theory and methodology in science and engineering (Vol. 150, pp. 120-131). New York: Wiley.

Chandrasekhar, C. K., Bagyalakshmi, H., Srinivasan, M. R., & Gallo, M. (2016). Partial ridge regression under multicollinearity. Journal of Applied Statistics, 43(13), 2462-2473.

Dorugade, A. V. (2014). New ridge parameters for ridge regression. Journal of the Association of Arab Universities for Basic and Applied Sciences, 15, 94-99.

Draper, N. R., & Smith, H. (2014). Applied regression analysis. John Wiley & Sons.

Kibria, B. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics-Simulation and Computation, 32(2), 419-435.

Guilkey, D. K., & Murphy, J. L. (1975). Directed ridge regression techniques in cases of multicollinearity. Journal of the American Statistical Association, 70(352), 769-775.

Montgomery, D. C., Peck, E. A., & Vining, G. G. (2015). Introduction to linear regression analysis. John Wiley & Sons.

Newhouse, J. P., & Oman, S. D. (1971). An Evaluation of Ridge Estimators: A Report Prepared for United States Air Force Project Rand. Rand.

R Core Team (2014). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL

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