Interquantile shrinkage and variable selection for longitudinal data in regression models

• Published in: Science China. Mathematics Vol. 68; no. 7; pp. 1701 - 1726
• Main Authors: Wan, Chuang, Zhong, Wei, Li, Chenjing, Song, Xinyuan
• Format: Journal Article
• Language: English
• Published: Beijing Science China Press 01.07.2025; Springer Nature B.V
• Subjects: Applications of Mathematics; Asymptotic properties; Commonality; Efficiency; Mathematics; Mathematics and Statistics; Quantiles; Regression coefficients; Regression models; 62G08; 62J07; GEE; fused penalty; sparsity; 62F12; interquantile shrinkage; longitudinal data
• ISSN: 1674-7283; 1869-1862
• DOI: 10.1007/s11425-023-2342-0

We develop an interquantile shrinkage estimation method to examine the underlying commonality structure of regression coefficients across various quantile levels for longitudinal data in a data-driven manner. This method provides a deeper insight into the relationship between the response and covariates, leading to enhanced estimation efficiency and model interpretability. We propose a fused penalized generalized estimation equation (GEE) estimator with a non-crossing constraint, which automatically promotes constancy in estimates across neighboring quantiles. By accounting for within-subject correlation in longitudinal data, the GEE estimator improves estimation efficiency. We employ a nested alternating direction method of multiplier (ADMM) algorithm to minimize the regularized objective function. The asymptotic properties of the penalized estimators are established. Furthermore, in the presence of irrelevant predictors, we develop a doubly penalized GEE estimator to simultaneously select active variables and identify commonality across quantiles. Numerical studies demonstrate the superior performance of our proposed methods in terms of estimation efficiency. We illustrate the application of our methodologies by analyzing a longitudinal wage dataset.