Functional connectivity is defined as the undirected association between two or more functional magnetic resonance imaging (fMRI) time series. Increasingly, subject-level functional connectivity data have been used to predict and classify clinical outcomes and subject attributes. We propose a single-index model wherein response variables and sparse functional connectivity network valued predictors are linked by an unspecified smooth function in order to accommodate potentially nonlinear relationships. We exploit the network structure of functional connectivity by imposing meaningful sparsity constraints, which lead not only to the identification of association of interactions between regions with the response but also the assessment of whether or not the functional connectivity associated with a brain region is related to the response variable. We demonstrate the effectiveness of the proposed model in simulation studies and in an application to a resting-state fMRI data set from the Human Connectome Project to model fluid intelligence and sex and to identify predictive links between brain regions.

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