Multi-directional variable selection of partially linear models with longitudinal data

In this paper, we investigate the 问题 of variable selection in personalized partially linear models for longitudinal data, integrating a multi-directional penalty function to achieve individualized variable selection and subgroup identification of heterogeneous covariates. The multi-directional penalty function allows for different groupings based on various covariate indicators, enhancing the efficiency of individualized estimation and the accuracy of variable selection. Moreover, this paper employs a profile local polynomial smoothing method for model estimation. Under some regularity 条件, we establish the asymptotic properties of parametric and nonparametric estimators, achieving variable selection and subgroup identification consistency. In this paper, we also present an efficient ADMM (alternating direction method of multipliers) algorithm to implement the proposed method, and investigate the convergence, convergence rate, and computational complexity of the proposed algorithm from both theoretical and simulation perspectives. Simulation studies show that the proposed method has better performance in terms of parameter estimation and variable selection compared with existing penalized estimators. We further apply the proposed method for analyzing the liver cirrhosis dataset to demonstrate its superior performance.