The Stability of Behavioral PLS Results in Ill-Posed Neuroimaging Problems

Behavioral Partial-Least Squares (PLS) is often used to analyze ill-posed functional Magnetic Resonance Imaging (f MRI) datasets, for which the number of variables are far larger than the number of observations. This procedure generates a latent variable (LV) brain map, showing brain regions that are most correlated with behavioral measures. The strength of the behavioral relationship is measured by the correlation between behavior and LV scores in the data. For standard behavioral PLS, bootstrap resampling is used to evaluate the reliability of the the brain LV and its behavioral correlations. However, the bootstrap may provide biased measures of the generalizability of results across independent datasets. We used split-half resampling to obtain unbiased measures of brain-LV reproducibility and behavioral prediction of the PLS model, for independent data. We show that bootstrapped PLS gives biased measures of behavioral correlations, whereas split-half resampling identifies highly stable activation peaks across single resampling splits. The ill-posed PLS solution can also be improved by regularization; we consistently improve the prediction accuracy and spatial reproducibility of behavioral estimates by (1) projecting f MRI data onto an optimized PCA basis, and (2) optimizing data preprocessing on an individual subject basis. These results show that significant improvements in generalizability and brain pattern stability are obtained with split-half versus bootstrapped resampling of PLS results, and that model performance can be further improved by regularizing the input data.