  Spatially varying directional data are routinely observed in several modern
applications such as meteorology, biology, geophysics, and engineering, etc.
However, only a few approaches are available for covariate-dependent
statistical analysis for such data. To address this gap, we propose a novel
generalized linear model to analyze such that using a von Mises Fisher (vMF)
distributed error structure. Using a novel link function that relies on the
transformation between Cartesian and spherical coordinates, we regress the
vMF-distributed directional data on the external covariates. This regression
model enables us to quantify the impact of external factors on the observed
directional data. Furthermore, we impose the spatial dependence using an
autoregressive model, appropriately accounting for the directional dependence
in the outcome. This novel specification renders computational efficiency and
flexibility. In addition, a comprehensive Bayesian inferential toolbox is
thoroughly developed and applied to our analysis. Subsequently, employing our
regression model to the Alzheimer's Disease Neuroimaging Initiative (ADNI)
data, we gain new insights into the relationship between cognitive impairment
and the orientations of brain fibers along with examining empirical efficacy
through simulation experiments.
