  The aim of this paper is to develop a class of spatial transformation models
(STM) to spatially model the varying association between imaging measures in a
three-dimensional (3D) volume (or 2D surface) and a set of covariates. Our STMs
include a varying Box-Cox transformation model for dealing with the issue of
non-Gaussian distributed imaging data and a Gaussian Markov Random Field model
for incorporating spatial smoothness of the imaging data. Posterior computation
proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and
real data analysis demonstrate that the STM significantly outperforms the
voxel-wise linear model with Gaussian noise in recovering meaningful geometric
patterns. Our STM is able to reveal important brain regions with morphological
changes in children with attention deficit hyperactivity disorder.
