A1824
Title: Disentangling location and concentration effects in von Mises-Fisher regression
Authors: Kipoong Kim - Changwon National University (Korea, South) [presenting]
Sungkyu Jung - Seoul National University (Korea, South)
Joern Schulz - University of Stavanger (Norway)
Abstract: In many problems the response of interest is a direction, that is, a point on the surface of a sphere. In regression with a spherical response, a covariate can affect the response in two ways, as in ordinary regression: it can move the mean direction, a location effect, and it can change how concentrated the response is around that direction, a concentration effect. Existing methods fall into two groups: spherical regression methods report a single coefficient for each covariate and so mix the two effects, whereas several testing methods provide a separate test for each effect but cannot adjust for other covariates. A generalized linear model is proposed that links the natural parameter of the von Mises-Fisher distribution linearly to the covariates. This reparameterization puts the density in canonical exponential-family form, so the maximum likelihood estimator is consistent and asymptotically normal under mild conditions. The contribution is a projection-based inference framework: projecting the estimated coefficient onto the estimated reference direction and onto its orthogonal complement yields separate test statistics for the location and concentration effects. Simulation studies show that the location and concentration tests keep the Type I error rate at the nominal level while attaining comparable power. The method was also applied to hippocampal shape data from the ParkWest study of Parkinson's disease.
