Permutation inference for canonical correlation analysis

Authors

Anderson M. Winkler, The University of Texas Rio Grande ValleyFollow
Olivier Renaud
Stephen M. Smith
Thomas E. Nichols

Document Type

Article

Publication Date

10-15-2020

Abstract

Canonical correlation analysis (CCA) has become a key tool for population neuroimaging, allowing investigation of associations between many imaging and non-imaging measurements. As age, sex and other variables are often a source of variability not of direct interest, previous work has used CCA on residuals from a model that removes these effects, then proceeded directly to permutation inference. We show that a simple permutation test, as typically used to identify significant modes of shared variation on such data adjusted for nuisance variables, produces inflated error rates. The reason is that residualisation introduces dependencies among the observations that violate the exchangeability assumption. Even in the absence of nuisance variables, however, a simple permutation test for CCA also leads to excess error rates for all canonical correlations other than the first. The reason is that a simple permutation scheme does not ignore the variability already explained by previous canonical variables. Here we propose solutions for both problems: in the case of nuisance variables, we show that transforming the residuals to a lower dimensional basis where exchangeability holds results in a valid permutation test; for more general cases, with or without nuisance variables, we propose estimating the canonical correlations in a stepwise manner, removing at each iteration the variance already explained, while dealing with different number of variables in both sides. We also discuss how to address the multiplicity of tests, proposing an admissible test that is not conservative, and provide a complete algorithm for permutation inference for CCA.

Comments

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

Recommended Citation

Winkler, A. M., Renaud, O., Smith, S. M., & Nichols, T. E. (2020). Permutation inference for canonical correlation analysis. NeuroImage, 220, 117065. https://doi.org/10.1016/j.neuroimage.2020.117065

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

First Page

117065

Publication Title

NeuroImage

DOI

10.1016/j.neuroimage.2020.117065

Academic Level

faculty

Mentor/PI Department

Office of Human Genetics