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

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 imp...

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Veröffentlicht in:Computational statistics Jg. 29; H. 6; S. 1515 - 1541
Hauptverfasser: Jou, Yow-Jen, Huang, Chien-Chia Liäm, Cho, Hsun-Jung
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2014
Springer Nature B.V
Schlagworte:
Collinearity
Computational mathematics
Economic models
Economic statistics
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Estimators
Inflation
Mathematical models
Mathematics and Statistics
Optimization
Original Paper
Perturbation methods
Probability and Statistics in Computer Science
Probability Theory and Stochastic Processes
Regression
Regression analysis
Statistics
Studies
Variables
Volatility
Convex optimization
Multicollearity
Variance inflation factor
ISSN:0943-4062, 1613-9658
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Zusammenfassung: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 VIF s, 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.
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ISSN:0943-4062
1613-9658
DOI:10.1007/s00180-014-0504-3