Variable Selection for Mixed Panel Count Data Using Gaussian Seamless-L0 Penalty

This paper considers variable selection for mixed panel count data, which frequently occur in longitudinal studies and whose analysis is quite challenging due to their complex data structures. For the problem, we propose a penalised likelihood procedure with the use of Gaussian Seamless-L-0 penalty under a proportional mean model. For its implementation, a computationally efficient EM algorithm is developed that enables sparse variable selection while ensuring accurate parameter estimation. The resulting estimator is shown to have the oracle property, and a simulation study is performed and confirms the strong finite-sample performance of the proposed method. Finally we apply the proposed approach to a set of real data on medical non-adherence arising from the Sequenced Treatment Alternatives to Relieve Depression Study and identify some new risk factors.