Multi-step methods for choosing the best set of variables in regression analysis

Authors:
Hiroshi Konno;Yoshihiro Takaya
Affiliations:
Department of Industrial and Systems Engineering, Chuo University, Tokyo, Japan;Department of Industrial and Systems Engineering, Chuo University, Tokyo, Japan
Venue:
Computational Optimization and Applications
Year:
2010

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Abstract

In a recent article (Konno and Yamamoto in ISE 07-01, Department of Industrial and Systems Engineering, Chuo University, February 2007), one of the authors formulated the problem of choosing the best set of explanatory variables from a large number of candidate variables in a linear regression model as a mixed 0---1 integer linear programming problem and showed that it can be solved by the state-of-the-art integer programming software.In this paper, we will propose multi-step methods for calculating a close to optimal solution of the problem which may not be solved by a single-step method presented in Konno and Yamamoto (ISE 07-01, Department of Industrial and Systems Engineering, Chuo University, February 2007). It will be shown that a multi-step method can generate a nearly optimal solution within a fraction of computation time of the single step method.Also, we will demonstrate that the best set of variables in terms of the squared error can be recovered under normality assumption.