This paper studies the problem of modeling relationship between two spherical (or
directional) random variables. Here the predictor and the response variables are 
constrained to be on a unit sphere and due to this nonlinear condition, the standard Euclidean regression models do not apply. Several past papers have studied this problem,
termed spherical regression, by modeling the response variable with a von Mises-Fisher
distribution with the mean given by a rotation of the predictor variable. The few papers
that go beyond rigid rotations have been limited to one- or two-dimensional spheres.
This paper extends the mean transformations to a larger group - the projective linear
group - on unit spheres of arbitrary dimensions, while keeping the von Mises-Fisher
distribution to model the noise. It develops a Newton-Raphson algorithm on special
linear group for finding maximum likelihood estimates of the regression parameter and
establishes asymptotic properties of these estimators using large sample-size analysis.
Through a variety of experiments, using data taken from projective shape analysis,
cloud tracking, etc, and some simulated datasets, this paper demonstrates improvements
in the prediction and modeling performance of the proposed framework over
previously used models