Plug‐in machine learning for partially linear mixed‐effects models with repeated measurements
提出一种即插即用机器学习方法，用于重复测量部分线性混合效应模型中的线性系数估计，该方法能处理复杂交互、非光滑项和高维变量，且估计量具有参数收敛速度和渐近正态性，在模拟和HIV纵向数据中表现优于惩罚样条方法。
Abstract Traditionally, spline or kernel approaches in combination with parametric estimation are used to infer the linear coefficient (fixed effects) in a partially linear mixed‐effects model for repeated measurements. Using machine learning algorithms allows us to incorporate complex interaction structures, nonsmooth terms, and high‐dimensional variables. The linear variables and the response are adjusted nonparametrically for the nonlinear variables, and these adjusted variables satisfy a linear mixed‐effects model in which the linear coefficient can be estimated with standard linear mixed‐effects methods. We prove that the estimated fixed effects coefficient converges at the parametric rate, is asymptotically Gaussian distributed, and semiparametrically efficient. Two simulation studies demonstrate that our method outperforms a penalized regression spline approach in terms of coverage. We also illustrate our proposed approach on a longitudinal dataset with HIV‐infected individuals. Software code for our method is available in the R ‐package dmlalg .