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

Abstract

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.

Scale‐free brain dynamics under physical and psychological distress: Pre‐treatment effects in women diagnosed with breast cancer

“…This multivariate procedure finds the pattern of brain voxels that shows greatest covariance between H and behavioral PC u i . The split‐half bPLS (see [Churchill et al, ] for details), produces (1) a reproducible Z ‐scored brain SPM, indicating brain voxels of reliable covariance with the behavioral PC, (2) a vector of latent variable scores w i , measuring how much each subject expresses the behavioral SPM pattern, and (3) and an unbiased predictive correlation ρ = corr( w i , v i ) of brain pattern expression versus behavior. We performed 200 resamples for bPLS analysis of each behavioral PC, to estimate an empirical 95% confidence interval on ρ .…”

Physical Activity, Mediterranean Diet and Biomarkers-Assessed Risk of Alzheimer’s: A Multi-Modality Brain Imaging Study

“…The General Linear Model (GLM) and χ 2 tests were used to compare clinical and demographical measures across LTA and MeDi groups (p < 0.05). Multivariate Partial Least Squares (PLS) regression analysis as implemented in PLS v1.0 was used for image analysis to compare LTA (LTA+ vs. LTA−), MeDi (MeDi+ vs. MeDi−) and LTA × MeDi combinations [ 33 ]-[ 35 ]. PLS regression is a multivariate extension of the multiple linear regression model that is used to construct predictive models when the number of variables (e.g., voxels) are far larger than the number of observations (e.g.…”

“…PLS regression is a multivariate extension of the multiple linear regression model that is used to construct predictive models when the number of variables (e.g., voxels) are far larger than the number of observations (e.g. subjects), and multi-collinear, as previously described [ 33 ]-[ 35 ]. Briefly, while univariate analysis is used to identify reliable signal changes at the level of individual image elements ( i.e.…”

White matter during concussion recovery: Comparing diffusion tensor imaging (DTI) and neurite orientation dispersion and density imaging (NODDI)

“…This is an extension of standard PLS (Krishnan, Williams, McIntosh, & Abdi, 2011), which identifies latent covariance relationships between brain imaging and behavioral data. As a latent variable model, it is also robust to high-dimensional, highly-correlated data (Churchill et al, 2013), where standard regression methods may be ill-posed and require careful regularization for a stable solution. This model was used to test for white matter regions showing simultaneous effects of concussion for the 6 DTI/NODDI parameters.…”

“…The approach has greater sensitivity than univariate methods, as NPLS can detect distributed patterns in the brain and leverage shared information across diffusion parameters. As a latent variable model, it is also robust to high-dimensional, highly-correlated data(Churchill et al, 2013), where standard regression methods may be ill-posed and require careful regularization for a stable solution.The NPLS model is described below.In neuroimaging PLS, two multivariate datasets are analyzed for subjects s = 1…S, including a (V × 1) vector of voxel values x s (e.g., a diffusion parameter map) and a (B × 1) vector of behavioral values y s (e.g., condition labels or clinical variables). The model quantifies shared information between x and y, by decomposing the data into k = 1…K…”