# Model Selection in Linear Mixed Models

arXiv: https://arxiv.org/abs/1306.2427 · HTML: https://mlsanity.com/paper/1306.2427/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2013.

## Built on by (most cited first, 2 of 2)

- [Subset selection for linear mixed models](https://mlsanity.com/paper/2107.12890/) (2021)
- [Gradient Boosted Mixed Models: Flexible Estimation of Mean and Variance Components for Clustered Data](https://mlsanity.com/paper/2511.00217/) (2025)

## Abstract (arXiv)

Linear mixed effects models are highly flexible in handling a broad range of data types and are therefore widely used in applications. A key part in the analysis of data is model selection, which often aims to choose a parsimonious model with other desirable properties from a possibly very large set of candidate statistical models. Over the last 5-10 years the literature on model selection in linear mixed models has grown extremely rapidly. The problem is much more complicated than in linear regression because selection on the covariance structure is not straightforward due to computational issues and boundary problems arising from positive semidefinite constraints on covariance matrices. To obtain a better understanding of the available methods, their properties and the relationships between them, we review a large body of literature on linear mixed model selection. We arrange, implement, discuss and compare model selection methods based on four major approaches: information criteria such as AIC or BIC, shrinkage methods based on penalized loss functions such as LASSO, the Fence procedure and Bayesian techniques.