Mixed integer quadratic optimization formulations for eliminating multicollinearity based on variance inflation factor

Ryuta Tamura, Ken Kobayashi, Yuichi Takano, Ryuhei Miyashiro (), Kazuhide Nakata and Tomomi Matsui
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Ryuta Tamura: Tokyo University of Agriculture and Technology
Ken Kobayashi: Fujitsu Laboratories Ltd.
Yuichi Takano: Senshu University
Ryuhei Miyashiro: Tokyo University of Agriculture and Technology
Kazuhide Nakata: Tokyo Institute of Technology
Tomomi Matsui: Tokyo Institute of Technology

Journal of Global Optimization, 2019, vol. 73, issue 2, No 9, 446 pages

Abstract: Abstract Multicollinearity exists when some explanatory variables of a multiple linear regression model are highly correlated. High correlation among explanatory variables reduces the reliability of the analysis. To eliminate multicollinearity from a linear regression model, we consider how to select a subset of significant variables by means of the variance inflation factor (VIF), which is the most common indicator used in detecting multicollinearity. In particular, we adopt the mixed integer optimization (MIO) approach to subset selection. The MIO approach was proposed in the 1970s, and recently it has received renewed attention due to advances in algorithms and hardware. However, none of the existing studies have developed a computationally tractable MIO formulation for eliminating multicollinearity on the basis of VIF. In this paper, we propose mixed integer quadratic optimization (MIQO) formulations for selecting the best subset of explanatory variables subject to the upper bounds on the VIFs of selected variables. Our two MIQO formulations are based on the two equivalent definitions of VIF. Computational results illustrate the effectiveness of our MIQO formulations by comparison with conventional local search algorithms and MIO-based cutting plane algorithms.

Keywords: Integer programming; Subset selection; Multicollinearity; Variance inflation factor; Multiple linear regression; Statistics (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10898-018-0713-3

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