# PLS and Functional Neuroimaging: Bias and Detection Power Across Different Resampling Schemes

## Abstract

Correlation Partial-Least Squares (PLSC) provides a robust model for analyzing functional neuroimaging data, which is used to identify functional brain networks that show the largest covariance with task stimuli. However, neuroimaging data tend to be high-dimensional (i.e., there are far more variables *P* than samples *N*), with significant noise confounds and variability in brain response. It is therefore challenging to identify the significant, stable components of PLSC analysis. Empirical significance estimators are widely used, as they make minimal assumptions about data structure. The most common estimator in neuroimaging PLS is Bootstrapped Variance (BV), which tests whether bootstrap-stabilized mean component eigenvalues (i.e., covariance) are significantly different from a permuted null distribution; however, recent studies have highlighted issues with this model. Two alternatives were proposed that instead focus on reliability of the PLSC saliences (i.e., singular vectors): a Split-half Stability (SS) model that measures the consistency of reconstructed components for split-half data, and Split-half Reproducibility (SR) which measures the reliability across independent split-half analyses. We compare BV, SS, and SR estimators on functional Magnetic Resonance Imaging (*f* MRI) data, for both simulated and experimental datasets. The SS and SR methods have comparable sensitivity in detecting “brain” components for most simulated and experimental conditions. However, SR shows consistently greater sensitivity for “task” components. We demonstrate that this is due to relative bias in the SS model: both “brain” and “task” components have biased null distributions, but for the low-dimensional “task” vectors, this bias becomes sufficiently high that it is often impossible to distinguish a significant effect from the null distribution.

## Keywords

*f*mri Behavioral pls Bootstrap Split-half resampling Prediction Reproducibility pca

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