Standardization of Variables and Collinearity Diagnostic in Ridge Regression

By José García, Román Salmerón, Catalina Beatriz García García, M. M. L. López Martín. 2016

51 citations recorded by the source corpus.

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

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/78c15ff384c92a13b732ecd05b45366de01d0683

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Citations in the corpus

The VIF and MSE in Raise Regression (2020, methodology): “[26], transforming the variable Xi as xi = Xi − ai bi , ai ∈ R, bi ∈ R− {0}, i = 2, .”
Collinearity diagnostic applied in ridge estimation through the variance inflation factor (2016, background): “However, the expression obtained for the VIF(λ) (see [23] for the case of two variables) does not satisfy the condition of being larger than one (see [11,13,31]).”
Variance Inflation Factor and Condition Number in multiple linear regression (2018, background): “Contrarily, the value of the CN depends on the data transformation [22,23].”