A Redefined Variance Inflation Factor: Overcoming the Limitations of the Variance Inflation Factor

A Redefined Variance Inflation Factor: Overcoming the Limitations of the Variance Inflation Factor

30 March 2024 | Román Salmerón-Gómez · Catalina B. García-García · José García-Pérez
The variance inflation factor (VIF) is a widely used tool for diagnosing multicollinearity in multiple linear regression models. However, it has several limitations: it only detects relationships between independent variables without considering the intercept, is not suitable for binary variables, and the orthogonal model used to calculate VIF is controversial. This paper introduces a redefined variance inflation factor (RVIF) that overcomes these limitations. The RVIF is implemented in the rvif R package, which provides a Monte Carlo simulation to establish thresholds for this new measure. The paper illustrates the RVIF's effectiveness through various examples and compares it with the *vif* command from the car R package, suggesting that non-statisticians should be warned about the potential issues with the traditional VIF. The introduction highlights the importance of identifying multicollinearity, especially when it affects the stability of OLS estimators, and discusses the limitations of the VIF, particularly in the context of binary variables and the intercept. The paper proposes a QR decomposition to address these issues and improve the reliability of multicollinearity detection.The variance inflation factor (VIF) is a widely used tool for diagnosing multicollinearity in multiple linear regression models. However, it has several limitations: it only detects relationships between independent variables without considering the intercept, is not suitable for binary variables, and the orthogonal model used to calculate VIF is controversial. This paper introduces a redefined variance inflation factor (RVIF) that overcomes these limitations. The RVIF is implemented in the rvif R package, which provides a Monte Carlo simulation to establish thresholds for this new measure. The paper illustrates the RVIF's effectiveness through various examples and compares it with the *vif* command from the car R package, suggesting that non-statisticians should be warned about the potential issues with the traditional VIF. The introduction highlights the importance of identifying multicollinearity, especially when it affects the stability of OLS estimators, and discusses the limitations of the VIF, particularly in the context of binary variables and the intercept. The paper proposes a QR decomposition to address these issues and improve the reliability of multicollinearity detection.
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