Evaluating permutation-based inference for partial least squares analysis of neuroimaging data

Partial least squares (PLS) is actively leveraged in neuroimaging work, typically to map latent variables (LVs) representing brain-behaviour associations. LVs are considered statistically significant if they tend to capture more covariance than LVs derived from permuted data, with a Procrustes rotation applied to map each set of permuted LVs to the space defined by the originals, creating an "apples to apples" comparison. Yet, it has not been established whether applying the rotation makes the permutation test more sensitive to whether true LVs are present in a dataset, and it is unclear whether significance alone is sufficient to fully characterize a PLS decomposition, given that complementary metrics such as strength and split-half stability may offer non-redundant information about the LVs. Accordingly, we performed PLS analyses across a range of simulated datasets with known latent effects, observing that the Procrustes rotation systematically weakened the null distributions for the first LV. By extension, the first LV was nearly always significant, regardless of whether the effect was weak, undersampled, noisy, or simulated at all. But, if no rotation was applied, all possible LVs tended to be significant as we increased the sample size of UK Biobank datasets. Meanwhile, LV strength and stability metrics accurately tracked our confidence that effects were present in simulated data, and allowed for a more nuanced assessment of which LVs may be relevant in the UK Biobank. We end by presenting a list of considerations for researchers implementing PLS permutation testing, and by discussing promising alternative tests which may alleviate the concerns raised by our findings.