Standardization of Variables and Collinearity Diagnostic in Ridge Regression

作者: José García , Román Salmerón , Catalina García , María del Mar López Martín

DOI: 10.1111/INSR.12099

关键词:

摘要: Summary Ridge estimation (RE) is an alternative method to ordinary least squares when there exists a collinearity problem in linear regression model. The variance inflator factor (VIF) applied test if the original model and also necessary after applying ridge estimate check chosen value for parameter k has mitigated problem. This paper shows that application of data working with leads non-monotone VIF values. Garcia et al. (2014) showed some problems traditional used RE. We propose augmented VIF, VIFR(j,k), associated RE, which obtained by standardizing before augmenting VIFR(j,k) will coincide estimator = 0. very desirable properties being continuous, monotone higher than one.

参考文章(28)
Donald R. Jensen, Donald E. Ramirez, Anomalies in Ridge Regression: Rejoinder International Statistical Review. ,vol. 78, pp. 215- 217 ,(2010) , 10.1111/J.1751-5823.2010.00116.X
John Fox, Georges Monette, Generalized Collinearity Diagnostics Journal of the American Statistical Association. ,vol. 87, pp. 178- 183 ,(1992) , 10.1080/01621459.1992.10475190
Andrew R. Willan, Donald G. Watts, Meaningful Multicollinearity Measures Technometrics. ,vol. 20, pp. 407- 412 ,(1978) , 10.1080/00401706.1978.10489694
Gary Smith, Frank Campbell, A Critique of Some Ridge Regression Methods Journal of the American Statistical Association. ,vol. 75, pp. 74- 81 ,(1980) , 10.1080/01621459.1980.10477428
Sylvain Sardy, On the Practice of Rescaling Covariates International Statistical Review. ,vol. 76, pp. 285- 297 ,(2008) , 10.1111/J.1751-5823.2008.00050.X
José Dias Curto, José Castro Pinto, The corrected VIF (CVIF) Journal of Applied Statistics. ,vol. 38, pp. 1499- 1507 ,(2011) , 10.1080/02664763.2010.505956
Arthur E. Hoerl, Robert W. Kennard, Ridge Regression: Applications to Nonorthogonal Problems Technometrics. ,vol. 12, pp. 69- 82 ,(1970) , 10.1080/00401706.1970.10488635
C.B. García, J. García, M.M. López Martín, R. Salmerón, Collinearity: revisiting the variance inflation factor in ridge regression Journal of Applied Statistics. ,vol. 42, pp. 648- 661 ,(2015) , 10.1080/02664763.2014.980789