title: Permutation inference for the general linear model.
abstract: Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. We present a generic framework for permutation inference for complex general linear models (GLMS) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. We also demonstrate how the inference on GLM parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm - the "randomise" algorithm - for permutation inference with the GLM.
authors: Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, UK; Global Imaging Unit, GlaxoSmithKline, London, UK; Department of Psychiatry, Yale University School of Medicine, New Haven, CT, USA. Electronic address: winkler@fmrib.ox.ac.uk.
authors: Anderson M
authors: AM
authors: Winkler
authors: Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, London, UK.
authors: Gerard R
authors: GR
authors: Ridgway
authors: Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, UK.
authors: Matthew A
authors: MA
authors: Webster
authors: Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, UK.
authors: Stephen M
authors: SM
authors: Smith
authors: Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, UK; Department of Statistics & Warwick Manufacturing Group, University of Warwick, Coventry, UK.
authors: Thomas E
authors: TE
authors: Nichols
mesh_terms: D000465:Algorithms; D000818:Animals; D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016014:Linear Models; D009415:Nerve Net / Q000502:physiology*; D012107:Research Design
keywords: General linear model; Multiple regression; Permutation inference; Randomise