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For Huntington disease, identification of brain regions related to motor impairment can be useful for developing interventions to alleviate the motor symptom, the major symptom of the disease. However, the effects from the brain regions to motor impairment may vary for different groups of patients. Hence, our interest is not only to identify the brain regions but also to understand how their effects on motor impairment differ by patient groups. This can be cast as a model selection problem for a varying‐coefficient regression. However, this is challenging when there is a pre‐specified group structure among variables. We propose a novel variable selection method for a varying‐coefficient regression with such structured variables and provide a publicly available R package svreg for implementation of our method. Our method is empirically shown to select relevant variables consistently. Also, our method screens irrelevant variables better than existing methods. Hence, our method leads to a model with higher sensitivity, lower false discovery rate and higher prediction accuracy than the existing methods. Finally, we found that the effects from the brain regions to motor impairment differ by disease severity of the patients. To the best of our knowledge, our study is the first to identify such interaction effects between the disease severity and brain regions, which indicates the need for customized intervention by disease severity.

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We improve upon the two-stage sparse vector autoregression (sVAR) method in Davis et al. (2016) by proposing an alternative two-stage modified sVAR method which relies on time series graphical lasso to estimate sparse inverse spectral density in the first stage, and the second stage refines non-zero entries of the AR coefficient matrices using a false discovery rate (FDR) procedure. Our method has the advantage of avoiding the inversion of the spectral density matrix but has to deal with optimization over Hermitian matrices with complex-valued entries. It significantly improves the computational time with a little loss in forecasting performance. We study the properties of our proposed method and compare the performance of the two methods using simulated and a real macro-economic dataset. Our simulation results show that the proposed modification or msVAR is a preferred choice when the goal is to learn the structure of the AR coefficient matrices while sVAR outperforms msVAR when the ultimate task is forecasting.

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