A VIF-based optimization model to alleviate collinearity problems in multiple linear regression

Yow Jen Jou, Chien Chia Liäm Huang*, Hsun-Jung Cho

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

In this paper, we address data collinearity problems in multiple linear regression from an optimization perspective. We propose a novel linearly constrained quadratic programming model, based on the concept of the variance inflation factor (VIF). We employ the perturbation method that involves imposing a general symmetric non-diagonal perturbation matrix on the correlation matrix. The proposed VIF-based model reduces the largest VIF by minimizing the resulting biases. The VIF-based model can mitigate the harm from data collinearity through the reduction in both the condition number and VIFs, meanwhile improving the statistical significance. The resulting estimator has bounded biases under an iterative framework and hence is termed the least accumulative bias estimator. Certain potential statistical properties can be further considered as the side constraints for the proposed model. Various numerical examples validate the proposed approach.

Original languageEnglish
Pages (from-to)1515-1541
Number of pages27
JournalComputational Statistics
Volume29
Issue number6
DOIs
StatePublished - 15 Nov 2014

Keywords

  • Convex optimization
  • Multicollearity
  • Variance inflation factor

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