Unified Variable Selection for Varying Coefficient Models with Longitudinal Data

Variable selection for varying coefficient models includes the separation of varying and constant effects, and the selection of variables with nonzero varying effects and those with nonzero constant effects. This paper proposes a unified variable selection approach called the double-penalized quadratic inference functions method for varying coefficient models of longitudinal data. The proposed method can not only separate varying coefficients and constant coefficients, but also estimate and select the nonzero varying coefficients and nonzero constant coefficients. It is suitable for variable selection of linear models, varying coefficient models, and partial linear varying coefficient models. Under regularity conditions, the proposed method is consistent in both separation and selection of varying coefficients and constant coefficients. The obtained estimators of varying coefficients possess the optimal convergence rate of non-parametric function estimation, and the estimators of nonzero constant coefficients are consistent and asymptotically normal. Finally, the authors investigate the finite sample performance of the proposed method through simulation studies and a real data analysis. The results show that the proposed method performs better than the existing competitor.