Mapping the quantitative relationship between structure and function in the human brain is an important and challenging
problem. Numerous volumetric, surface, region of interest and voxelwise image processing techniques have been developed
to statistically assess potential correlations between imaging and non-imaging metrics. Recently, biological parametric
mapping has extended the widely popular statistical parametric approach to enable application of the general linear
model to multiple image modalities (both for regressors and regressands) along with scalar valued observations.
This approach offers great promise for direct, voxelwise assessment of structural and functional relationships with multiple
imaging modalities. However, as presented, the biological parametric mapping approach is not robust to outliers
and may lead to invalid inferences (e.g., artifactual low p-values) due to slight mis-registration or variation in anatomy
between subjects. To enable widespread application of this approach, we introduce robust regression and robust inference
in the neuroimaging context of application of the general linear model. Through simulation and empirical studies,
we demonstrate that our robust approach reduces sensitivity to outliers without substantial degradation in power. The
robust approach and associated software package provides a reliable way to quantitatively assess voxelwise correlations
between structural and functional neuroimaging modalities.