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Neuroimage. 2014 May 15;92:381-97. doi: 10.1016/j.neuroimage.2014.01.060. Epub 2014 Feb 11.

Permutation inference for the general linear model.

Author information

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:
Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, London, UK.
Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, UK.
Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, UK; Department of Statistics & Warwick Manufacturing Group, University of Warwick, Coventry, UK.


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.


General linear model; Multiple regression; Permutation inference; Randomise

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