Plug‐in machine learning for partially linear mixed‐effects models with repeated measurements

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.