  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 and
high-dimensional variables. We employ double machine learning to cope with the
nonparametric part of the partially linear mixed-effects model: the nonlinear
variables are regressed out nonparametrically from both the linear variables
and the response. This adjustment can be performed with any machine learning
algorithm, for instance random forests, which allows to take complex
interaction terms and nonsmooth structures into account. The adjusted variables
satisfy a linear mixed-effects model, where the linear coefficient can be
estimated with standard linear mixed-effects techniques. 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.
