  In this paper, we propose the use of geodesic distances in conjunction with
multivariate distance matrix regression, called geometric-MDMR, as a powerful
first step analysis method for manifold-valued data. Manifold-valued data is
appearing more frequently in the literature from analyses of earthquake to
analysing brain patterns. Accounting for the structure of this data increases
the complexity of your analysis, but allows for much more interpretable results
in terms of the data. To test geometric-MDMR, we develop a method to simulate
functional connectivity matrices for fMRI data to perform a simulation study,
which shows that our method outperforms the current standards in fMRI analysis.
