Multicollinearity Analysis and Variable/Model Selection in Regression

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K01431
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 07030:Economic statistics-related
• Research Institution: Nagoya University of Commerce & Business
• Principal Investigator: Kariya Takeaki 名古屋商科大学, マネジメント研究科, 教授 (70092624)
• Co-Investigator(Kenkyū-buntansha): 林 高樹 慶應義塾大学, 経営管理研究科(日吉), 教授 (80420826)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: linear regression model / model selection process / collinearity / OLS / effective modeling / VIF / principal component / decision theory

Outline of Final Research Achievements

In traditional regression model y=Xb +u with collinearity, based on X only, this research first defines the inefficiency risk measure I and collinearity (instability) measure C of each individual OLSE and a model is defined to be effective if I<c and C<d are satisfied uniformly controlled for given (c,d). Then we develop a model selection process (MSP) of finding a class H of effective sub-models. The risk measure (I, C) gives a partial ordering on the set H and so it also gives a decision-theoretic framework in comparing models with such concept of inadmissibility. It is shown that I = C =0 hold if and only if the columns of X are mutually orthogonal. Once the class H is obtained, an optimal model is obtained by applying such model selection criteria as AIC.
To get H, two algorithms are proposed: variable-increasing method and variable-decreasing method with principal component analysis.

Free Research Field

統計学

Academic Significance and Societal Importance of the Research Achievements

重共線性のもとでの有効な回帰モデル選択問題の研究課題の核心をなす学術的「問い」は、「現在の学術的状況では回帰分析の大きな狙いである因果実証性の検証可能性、実証的科学性をどこまで方法的に担保できるのか」、という問いであると考える。その意味で、この研究はこれまでの状況を異なる新しい代替的方法で大きく改善をしたことと考える。回帰分析の一つの教科書的な基礎を与えるものとなると考える。