# Sparse high-dimensional linear mixed modeling with a partitioned empirical Bayes ECM algorithm

arXiv: https://arxiv.org/abs/2310.12285 · HTML: https://mlsanity.com/paper/2310.12285/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 69 references that are in the map.
- First posted on arXiv 18 Oct 2023.

## Builds on (most cited first, 7 of 7)

- [Expectation propagation as a way of life: A framework for Bayesian inference on partitioned data](https://mlsanity.com/paper/1412.4869/) (2014)
- [Inference for high-dimensional linear mixed-effects models: A quasi-likelihood approach](https://mlsanity.com/paper/1907.06116/) (2019)
- [A Relaxation Approach to Feature Selection for Linear Mixed Effects Models](https://mlsanity.com/paper/2205.06925/) (2022)
- [Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm](https://mlsanity.com/paper/2209.08139/) (2022)
- [A scalable and efficient covariate selection criterion for mixed effects regression models with unknown random effects structure](https://mlsanity.com/paper/1612.00759/) (2016)
- [An iterative algorithm for joint covariate and random effect selection in mixed effects models](https://mlsanity.com/paper/1612.02405/) (2016)
- [Sparse Linear Mixed Model Selection via Streamlined Variational Bayes](https://mlsanity.com/paper/2110.07048/) (2021)

## Abstract (arXiv)

High-dimensional longitudinal data is increasingly used in a wide range of scientific studies. To properly account for dependence between longitudinal observations, statistical methods for high-dimensional linear mixed models (LMMs) have been developed. However, few packages implementing these high-dimensional LMMs are available in the statistical software R. Additionally, some packages 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. Supplementary materials are available online.