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Neighborhood search heuristics for selecting hierarchically well‐formulated subsets in polynomial regression

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  • Michael J. Brusco
  • Douglas Steinley

Abstract

The importance of subset selection in multiple regression has been recognized for more than 40 years and, not surprisingly, a variety of exact and heuristic procedures have been proposed for choosing subsets of variables. In the case of polynomial regression, the subset selection problem is complicated by two issues: (1) the substantial growth in the number of candidate predictors, and (2) the desire to obtain hierarchically well‐formulated subsets that facilitate proper interpretation of the regression parameter estimates. The first of these issues creates the need for heuristic methods that can provide solutions in reasonable computation time; whereas the second requires innovative neighborhood search approaches that accommodate the hierarchical constraints. We developed tabu search and variable neighborhood search heuristics for subset selection in polynomial regression. These heuristics are applied to a classic data set from the literature and, subsequently, evaluated in a simulation study using synthetic data sets. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010

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  • Michael J. Brusco & Douglas Steinley, 2010. "Neighborhood search heuristics for selecting hierarchically well‐formulated subsets in polynomial regression," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(1), pages 33-44, February.
    • Handle: RePEc:wly:navres:v:57:y:2010:i:1:p:33-44
    DOI: 10.1002/nav.20380
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    1. Cristian Gatu & Erricos Kontoghiorghes, 2002. "A branch and bound algorithm for computing the best subset regression models," Computing in Economics and Finance 2002 294, Society for Computational Economics.
    2. J. A. Nelder, 2000. "Functional marginality and response-surface fitting," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(1), pages 109-112.
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