Plug-in machine learning for partially linear mixed-effects models with repeated measurements
Open access
Date
2023-12Type
- Journal Article
ETH Bibliography
yes
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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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000614568Publication status
publishedExternal links
Journal / series
Scandinavian Journal of StatisticsVolume
Pages / Article No.
Publisher
WileySubject
between-group heterogeneity; CD4 dataset (HIV); dependent data; double machine learning; fixed effects estimation; longitudinal data; semiparametric estimationOrganisational unit
03502 - Bühlmann, Peter L. / Bühlmann, Peter L.
Funding
786461 - Statistics, Prediction and Causality for Large-Scale Data (EC)
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ETH Bibliography
yes
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