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Why do we still use stepwise modelling in ecology and behaviour?

Authors

  • MARK J. WHITTINGHAM,

    1. Division of Biology, School of Biology and Psychology, Ridley Building, University of Newcastle, Newcastle Upon Tyne, NE1 7RU, UK; Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK;
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  • PHILIP A. STEPHENS,

    1. Division of Biology, School of Biology and Psychology, Ridley Building, University of Newcastle, Newcastle Upon Tyne, NE1 7RU, UK; Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK;
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  • RICHARD B. BRADBURY,

    1. Royal Society for the Protection of Birds, The Lodge, Sandy, Bedfordshire, SG19 2DL, UK; and
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  • ROBERT P. FRECKLETON

    1. Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK
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M. J. Whittingham, Division of Biology, School of Biology and Psychology, Ridley Building, University of Newcastle, Newcastle Upon Tyne, NE1 7RU, UK. E-mail: m.j.whittingham@ncl.ac.uk

Summary

  • 1The biases and shortcomings of stepwise multiple regression are well established within the statistical literature. However, an examination of papers published in 2004 by three leading ecological and behavioural journals suggested that the use of this technique remains widespread: of 65 papers in which a multiple regression approach was used, 57% of studies used a stepwise procedure.
  • 2The principal drawbacks of stepwise multiple regression include bias in parameter estimation, inconsistencies among model selection algorithms, an inherent (but often overlooked) problem of multiple hypothesis testing, and an inappropriate focus or reliance on a single best model. We discuss each of these issues with examples.
  • 3We use a worked example of data on yellowhammer distribution collected over 4 years to highlight the pitfalls of stepwise regression. We show that stepwise regression allows models containing significant predictors to be obtained from each year's data. In spite of the significance of the selected models, they vary substantially between years and suggest patterns that are at odds with those determined by analysing the full, 4-year data set.
  • 4An information theoretic (IT) analysis of the yellowhammer data set illustrates why the varying outcomes of stepwise analyses arise. In particular, the IT approach identifies large numbers of competing models that could describe the data equally well, showing that no one model should be relied upon for inference.

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