Orthogonalization of regressors in fMRI models
Open accessAbstract
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.
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None of the predictors was orthogonalised.
“all predictors were convolved with the double-gamma haemodynamic response function and none of them was orthogonalised (Mumford et al., 2015).”
From Are prediction error modifications domain specific in autism but domain general in ADHD? (2025) · cites this paper as Mumford et al., 2015
The Conclusions and Discussion (page unavailable) say orthogonalization often confuses interpretation and should be used only when it improves interpretation, supporting a rationale for leaving predictors unorthogonalized. The paper does not establish whether the citing study actually orthogonalized any of its predictors. (LLM, conf=0.82)
Experimental — accuracy not yet measuredThe study employed a block design, which inherently introduces issues of collinearity.
“Third, we employed a block design, which inherently introduces issues of collinearity (Mumford et al., 2015).”
From Neural correlates of emotion acceptance<i>vs</i>worry or suppression in generalized anxiety disorder (2017) · cites this paper as Mumford et al., 2015
The Introduction explains how timing in an fMRI experiment can make regressors highly correlated, and Methods > Avoiding collinearity discusses reducing collinearity through study planning. These passages support the general concern about design-related collinearity, but do not say that a block design inherently introduces it. No page numbers are provided in our copy. (LLM, conf=0.82)
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- Authors
- Mumford, J. A., Poline, J.-B., & Poldrack, R. A.
- Affiliations
- University of Wisconsin–Madison (US)
- University of California, Berkeley (US)
- Stanford University (US)
- Corresponding author
- Mumford, Jeanette A.
- Venue
- PLoS ONE
- Publisher
- Public Library of Science (PLoS)
- Published
- 2015-04-28
- Volume
- 10
- Issue
- 4
- Pages
- e0126255
- ISSN
- 1932-6203 (ISSN-L)
- PMC
- PMC4412813
- OpenAlex
- W2013974533
- Cited by
- 276
- References
- 9
- Citations by year
- 2026: 16 · 2025: 27 · 2024: 24 · 2023: 22 · 2022: 29 · 2021: 26 · 2020: 38 · 2019: 16 · 2018: 29 · 2017: 32 · 2016: 15 · 2015: 2
- FWCI
- 15.63
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- PLoS ONE (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced MRI Techniques and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- orthogonalization, multicollinearity, parameter estimation, statistical power, SPM, FSL, design matrix
- MeSH terms
- Algorithms, Humans, Magnetic Resonance Imaging, Models, Theoretical, Reaction Time, Regression Analysis, Software
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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