Abstract
Many neuroscientists are interested in how connectomes (graphical representations of functional connectivity between areas of the brain) change in relation to covariates. In statistics, changes like this are analyzed using regression, where the outcomes or dependent variables are regressed onto the covariates. However, when the outcome is a complex object, such as connectome graphs, classical regression models cannot be used. The regression approach developed here to work with complex graph outcomes combines recursive partitioning with the Gibbs distribution. We will only discuss the application to connectomes, but the method is generally applicable to any graphical outcome. The method, called Gibbs-RPart, partitions the covariate space into a set of nonoverlapping regions such that the connectomes within regions are more similar than they are to the connectomes in other regions. This paper extends the object-oriented data analysis paradigm for graph-valued data based on the Gibbs distribution, which we have applied previously to hypothesis testing to compare populations of connectomes from distinct groups (see the work of La Rosa et al).