# Inference for high-dimensional linear mixed-effects models: A quasi-likelihood approach

arXiv: https://arxiv.org/abs/1907.06116 · HTML: https://mlsanity.com/paper/1907.06116/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2019.

## Built on by (most cited first, 3 of 3)

- [Double Machine Learning for Partially Linear Mixed-Effects Models with Repeated Measurements](https://mlsanity.com/paper/2108.13657/) (2021)
- [Sparse high-dimensional linear mixed modeling with a partitioned empirical Bayes ECM algorithm](https://mlsanity.com/paper/2310.12285/) (2023)
- [Deep Generalised Mixed Models: a Novel Neural Network Structure for Analysing Hierarchical Data](https://mlsanity.com/paper/2608.05930/) (2026)

## Abstract (arXiv)

Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional fixed effects. The proposed method is applicable to general settings where the dimension of the random effects and the cluster sizes are possibly large. Regarding the fixed effects, we provide rate optimal estimators and valid inference procedures that do not rely on the structural information of the variance components. We also study the estimation of variance components with high-dimensional fixed effects in general settings. The algorithms are easy to implement and computationally fast. The proposed methods are assessed in various simulation settings and are applied to a real study regarding the associations between body mass index and genetic polymorphic markers in a heterogeneous stock mice population.