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

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.

Automated summary

This paper focuses on the application of the Stewart index in detecting collinearity and aims to establish thresholds for judging worrisome collinearity issues. The study also attempts to extend the application of the Stewart index for use after ridge regression estimation, which is commonly used for models with multicollinearity. Through Monte Carlo simulation, the study relates the Stewart index to the condition number to address the issue of multicollinearity effectively.