Multivariate distance matrix regression for a manifold-valued response variable

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.