Obtaining a threshold for the stewart index and its extension to ridge regression

Ainara Rodríguez Sánchez (), Román Salmerón Gómez () and Catalina García García ()
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Ainara Rodríguez Sánchez: University of Granada
Román Salmerón Gómez: University of Granada
Catalina García García: University of Granada

Computational Statistics, 2021, vol. 36, issue 2, No 10, 1029 pages

Abstract: Abstract The linear regression model is widely applied to measure the relationship between a dependent variable and a set of independent variables. When the independent variables are related to each other, it is said that the model presents collinearity. If the relationship is between the intercept and at least one of the independent variables, the collinearity is nonessential, while if the relationship is between the independent variables (excluding the intercept), the collinearity is essential. The Stewart index allows the detection of both types of near multicollinearity. However, to the best of our knowledge, there are no established thresholds for this measure from which to consider that the multicollinearity is worrying. This is the main goal of this paper, which presents a Monte Carlo simulation to relate this measure to the condition number. An additional goal of this paper is to extend the Stewart index for its application after the estimation by ridge regression that is widely applied to estimate model with multicollinearity as an alternative to ordinary least squares (OLS). This extension could be also applied to determine the appropriate value for the ridge factor.

Keywords: Linear regression; Multicollinearity; Ridge regression; Stewart index (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00180-020-01047-2

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