Principal Components Decomposition of Fraction of Variance in High Dimensional Linear Models

Music City Center 

The fraction of variance explained (FVE) in a linear model quantifies the extent to which predictors account for outcome variability. In high dimensional settings, where traditional FVE estimators do not apply, modern FVE estimators such as GWASH struggle with strong correlation among predictors, often found, for example, in brain imaging data. We propose a decomposition framework that partitions the FVE into two components: a low dimensional component capturing the strong correlation, estimable by low dimensional methods, and a high dimensional component with remaining weak correlation, estimable by high dimensional methods. Simulations demonstrate that decomposition of dominant PCs improves bias reduction in FVE estimation compared to standard approaches, such as GCTA. Our method shows consistent performance asymptotically. Application to the Adolescent Brain Cognitive Development (ABCD) dataset validates its real-world applicability, capturing nuanced heritability signals in high-resolution brain imaging data. This work offers a robust framework for unbiased FVE estimation in high-dimensional models.

The fraction of variance explained (FVE)

brain imaging

high dimensional

principal component decomposition 

International Chinese Statistical Association