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

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 subse...

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Bibliographic Details
Published inJournal of global optimization Vol. 73; no. 2; pp. 431 - 446
Main Authors Tamura, Ryuta, Kobayashi, Ken, Takano, Yuichi, Miyashiro, Ryuhei, Nakata, Kazuhide, Matsui, Tomomi
Format Journal Article
LanguageEnglish
Published New York Springer US 15.02.2019
Springer
Springer Nature B.V
Subjects
Algorithms
Analysis
Computer Science
Formulations
Inflation (Finance)
Mathematics
Mathematics and Statistics
Mixed integer
Operations Research/Decision Theory
Optimization
Real Functions
Regression analysis
Regression models
Reliability analysis
Search algorithms
Upper bounds
Variance
Integer programming
Variance inflation factor
Multiple linear regression
Subset selection
Statistics
Multicollinearity
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Summary: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.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-018-0713-3