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Orthogonalization of Regressors in fMRI Models

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  • Jeanette A Mumford
  • Jean-Baptiste Poline
  • Russell A Poldrack

Abstract

The occurrence of collinearity in fMRI-based GLMs (general linear models) may reduce power or produce unreliable parameter estimates. It is commonly believed that orthogonalizing collinear regressors in the model will solve this problem, and some software packages apply automatic orthogonalization. However, the effects of orthogonalization on the interpretation of the resulting parameter estimates is widely unappreciated or misunderstood. Here we discuss the nature and causes of collinearity in fMRI models, with a focus on the appropriate uses of orthogonalization. Special attention is given to how the two popular fMRI data analysis software packages, SPM and FSL, handle orthogonalization, and pitfalls that may be encountered in their usage. Strategies are discussed for reducing collinearity in fMRI designs and addressing their effects when they occur.

Suggested Citation

  • Jeanette A Mumford & Jean-Baptiste Poline & Russell A Poldrack, 2015. "Orthogonalization of Regressors in fMRI Models," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-11, April.
    • Handle: RePEc:plo:pone00:0126255
    DOI: 10.1371/journal.pone.0126255
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    References listed on IDEAS

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    1. Robert O’brien, 2007. "A Caution Regarding Rules of Thumb for Variance Inflation Factors," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(5), pages 673-690, October.
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    1. Jaron T Colas & Wolfgang M Pauli & Tobias Larsen & J Michael Tyszka & John P O’Doherty, 2017. "Distinct prediction errors in mesostriatal circuits of the human brain mediate learning about the values of both states and actions: evidence from high-resolution fMRI," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-32, October.
    2. Nir Moneta & Mona M. Garvert & Hauke R. Heekeren & Nicolas W. Schuck, 2023. "Task state representations in vmPFC mediate relevant and irrelevant value signals and their behavioral influence," Nature Communications, Nature, vol. 14(1), pages 1-21, December.
    3. Johannes Algermissen & Jennifer C. Swart & René Scheeringa & Roshan Cools & Hanneke E. M. den Ouden, 2024. "Prefrontal signals precede striatal signals for biased credit assignment in motivational learning biases," Nature Communications, Nature, vol. 15(1), pages 1-19, December.
    4. Jordan Crivelli-Decker & Alex Clarke & Seongmin A. Park & Derek J. Huffman & Erie D. Boorman & Charan Ranganath, 2023. "Goal-oriented representations in the human hippocampus during planning and navigation," Nature Communications, Nature, vol. 14(1), pages 1-13, December.
    5. Laurens Winkelmeier & Carla Filosa & Renée Hartig & Max Scheller & Markus Sack & Jonathan R. Reinwald & Robert Becker & David Wolf & Martin Fungisai Gerchen & Alexander Sartorius & Andreas Meyer-Linde, 2022. "Striatal hub of dynamic and stabilized prediction coding in forebrain networks for olfactory reinforcement learning," Nature Communications, Nature, vol. 13(1), pages 1-21, December.

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