Estimation for High-Dimensional Linear Mixed-Effects Models Using ${\ell }_1$-Penalization

Abstract

We propose an ${\ell }_1$-penalized estimation procedure for high-dimensional linear mixed-effects models. The models are useful whenever there is a grouping structure among high-dimensional observations, i.e. for clustered data. We prove a consistency and an oracle optimality result and we develop an algorithm with provable numerical convergence. Furthermore, we demonstrate the performance of the method on simulated and a real high-dimensional data set.

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• Quasi-Likelihood and/or Robust Estimation in High Dimensions
• Double Machine Learning for Partially Linear Mixed-Effects Models with Repeated Measurements
• Improving the identification of antigenic sites in the H1N1 Influenza virus through accounting for the experimental structure in a sparse hierarchical Bayesian model
• Bayesian high-dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm
• Deep learning and differential equations for modeling changes in individual-level latent dynamics between observation periods
• Uniformly Valid Inference Based on the Lasso in Linear Mixed Models