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


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Article Info

DATE

2019-02

AUTHORS

Ryuta Tamura, Ken Kobayashi, Yuichi Takano, Ryuhei Miyashiro, Kazuhide Nakata, Tomomi Matsui

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. More... »

PAGES

1-16

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10898-018-0713-3

DOI

http://dx.doi.org/10.1007/s10898-018-0713-3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107767973


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