Robust Variance Inflation Factor: A Promising Approach for Collinearity Diagnostics in the Presence of Outliers

• Published in: Sankhyā. Series B (2008) Vol. 86; no. 2; pp. 845 - 871
• Main Authors: Jacob, Jinse, Varadharajan, R
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.11.2024
• Subjects: Mathematics and Statistics; Statistics; Outliers; VIF; 62J05; Multicollinearity; Robust Estimation; 62H20; RMSE; Projection Depth
• ISSN: 0976-8386; 0976-8394
• DOI: 10.1007/s13571-024-00342-y

Multicollinearity poses a significant hazard to the estimation process and interpretation of the models in regression analysis and the presence of outliers make the problem even worse. The Variance Inflation Factor (VIF), a most commonly used collinearity diagnostic tool, is susceptible to being biased as a result of the presence of outliers in the dataset. In this research, we propose the Robust Variance Inflation Factor (RVIF), which is resistant to the influence of outliers. The idea of Deepest Data Points (DDP) based on projection depth serves as the foundation for development of this study, and this enables the proposed method make more accurate and robust. An extensive simulation study has been carried out to evaluate the efficacy of the proposed strategy in comparison to the other approaches that already exist, by taking various factors which influence the behaviour of the estimator. As an evaluation metric, the Root Mean Squared Error (RMSE) is adopted. The results demonstrated that the depth-based RVIF method outperformed than other methods. Additionally, we provide an application of the RVIF in ridge parameter estimation.