Sparse functional varying-coefficient mixture regression

The functional varying-coefficient model (FVCM) provides a simple yet efficient method for function on scalar regression. However, classical FVCM typically assumes that varying associations between functional responses and scalar covariates are identical for all subjects and nonzero in the entire domain of functional measures. This study considers sparse functional varying-coefficient mixture regression, which allows heterogeneous regression associations and dependency structure among multiple functional responses and accommodates functional sparsity in varying coefficient functions. Moreover, we devise a computationally efficient EM algorithm with a double-sparse penalty for estimation. We show that the proposed estimator is consistent, can uncover sparse subregions, and simultaneously select the number of clusters with probability tending to one. Simulation studies and an application to the Alzheimer’s Disease Neuroimaging Initiative study confirm that the proposed method yields more interpretable results and a much lower classification error than existing methods.