High-dimensional longitudinal data is increasingly used in a wide range of
scientific studies. However, there are few statistical methods for
high-dimensional linear mixed models (LMMs), as most Bayesian variable
selection or penalization methods are designed for independent observations.
Additionally, the few available software packages for high-dimensional LMMs
suffer from scalability issues. This work presents an efficient and accurate
Bayesian framework for high-dimensional LMMs. We use empirical Bayes estimators
of hyperparameters for increased flexibility and an
Expectation-Conditional-Minimization (ECM) algorithm for computationally
efficient maximum a posteriori probability (MAP) estimation of parameters. The
novelty of the approach lies in its partitioning and parameter expansion as
well as its fast and scalable computation. We illustrate Linear Mixed Modeling
with PaRtitiOned empirical Bayes ECM (LMM-PROBE) in simulation studies
evaluating fixed and random effects estimation along with computation time. A
real-world example is provided using data from a study of lupus in children,
where we identify genes and clinical factors associated with a new lupus
biomarker and predict the biomarker over time