Jeff Goldsmith, Johns Hopkins School of Public HealthFebruary 21, 2012 @ 3:30 p.m. - 4:30 pm
Location: 701 Blockley Hall
Scalar-on-Function and Scalar-on-Image Regression
Motivated by a neuroimaging study of multiple sclerosis patients, we develop estimation methods for regression models in which the predictor of interest is either a function or an image. Although these models are linked conceptually, the estimation approaches are distinct. For scalar-on-function regression, the functional predictor is projected onto a large number of smooth eigenvectors and the coefficient function is estimated using penalized spline regression. For scalar-on-image regression, we combine an Ising prior distribution for a latent binary indicator image with an intrinsic Gaussian Markov random field prior for non-zero coefficients; the result is a sparse and smooth coefficient image. Both approaches are scalable and computationally feasible. Methods are applied to a study of white matter demyelination via diffusion tensor imaging in which various cerebral white matter tract properties are used to predict cognitive and motor function in multiple sclerosis patients.