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Home›Statistics›Robust Linear Mixed-Effects Model
Regression model

Robust Linear Mixed-Effects Model

Also known as: robust mixed-effects model, robust linear mixed model, robust LMM, Robust Karma Etkiler Modeli

The robust mixed model is a linear mixed-effects model for panel and repeated-measures data that tolerates outliers and heavy-tailed errors. It replaces the usual likelihood with bounded-influence estimating equations, building on the robust restricted maximum likelihood of Richardson and Welsh (1995) and the robustlmm implementation of Koller (2016).

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Robust Mixed Model
Heteroscedasticity-Robus…OLS RegressionPanel Fixed EffectsPermutation TestRobust RegressionMAD EstimationRobust Time Series Analy…Sn and Qn Scale Estimato…

When to use it

Use the robust mixed model when you have continuous outcomes with a panel or repeated-measures (clustered) structure and you suspect outliers or heavy-tailed, non-normal errors that would distort an ordinary mixed model. It assumes a genuine grouped structure is present and is designed precisely for the case where normality is doubtful. A reasonably large sample is needed — at least about 50 observations — because the variance components and robust scale must be estimated reliably.

Strengths & limitations

Strengths
  • Tolerates outliers and heavy-tailed errors that would bias an ordinary linear mixed model.
  • Does not require normally distributed errors, so it suits contaminated or skewed clustered data.
  • Respects the panel or repeated-measures structure through random effects while protecting both the fixed effects and the variance components from contamination.
Limitations
  • Needs a fairly large sample (at least about 50 observations); in small samples it can fail to converge.
  • When the outlier ratio is very high (above roughly 25%), the variance components can no longer be estimated reliably.
  • More computationally demanding and less standard than ordinary mixed models, and typically relies on specialised software.

Frequently asked

How is this different from an ordinary linear mixed model?

The model structure — fixed effects plus cluster-specific random effects — is identical. The difference is in estimation: the robust version replaces the Gaussian likelihood with bounded-influence estimating equations that downweight outliers, so a few extreme points cannot dominate the fixed effects or the variance components.

When should I prefer a permutation test instead?

In small samples (fewer than about 30 observations) the robust mixed model often struggles to converge. A permutation test sidesteps the variance-component estimation and is the safer choice when the sample is that small.

What if more than a quarter of my data are outliers?

With an outlier ratio above roughly 25%, the robust mixed model can no longer estimate the variance components reliably. In that regime bootstrap inference is more trustworthy than relying on the robust fit.

Does it require normally distributed errors?

No. The method is built precisely for heavy-tailed and non-normal errors. It assumes a genuine panel or repeated-measures structure and continuous outcomes, but it does not require the normality that an ordinary mixed model leans on.

Sources

  1. Koller, M. (2016). robustlmm: An R Package for Robust Estimation of Linear Mixed-Effects Models. Journal of Statistical Software, 75(6), 1-24. DOI: 10.18637/jss.v075.i06 ↗
  2. Richardson, A. M. & Welsh, A. H. (1995). Robust Restricted Maximum Likelihood in Mixed Linear Models. Biometrics, 51(4), 1429-1439. DOI: 10.2307/2533273 ↗

How to cite this page

ScholarGate. (2026, June 1). Robust Linear Mixed-Effects Model. ScholarGate. https://scholargate.app/en/statistics/robust-mixed-model

Related methods

Heteroscedasticity-Robust Standard ErrorsOLS RegressionPanel Fixed EffectsPermutation TestRobust Regression

Which method?

Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.

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Referenced by

MAD EstimationRobust Time Series AnalysisSn and Qn Scale Estimators

Similar methods

Robust Hierarchical Linear ModelMixed Effects ModelRobust Mixture ModelingRobust Multiple linear regressionRobust repeated measures ANOVARobust RegressionRobust Random Effects ModelBayesian Mixed Effects Model

Related reference concepts

Multilevel and Partial Pooling ModelsModel-Based ClusteringHierarchical Bayesian ModelsHyperpriors and ShrinkageLogistic DiscriminationMultivariate Multiple Regression

Spotted an issue on this page? Report or suggest a fix →

ScholarGate — Robust Mixed Model (Robust Linear Mixed-Effects Model). Retrieved 2026-07-21 from https://scholargate.app/en/statistics/robust-mixed-model · Dataset: https://doi.org/10.5281/zenodo.20539026
Quick facts
Originator
Richardson & Welsh (robust REML); Koller (robustlmm implementation)
Year
2016
Type
Robust linear mixed-effects model
Estimator
Robust REML / robust scoring with bounded influence functions
Outcome
continuous
DataStructure
panel or repeated-measures (clustered)
MinSample
50
Related methods
Heteroscedasticity-Robust Standard ErrorsOLS RegressionPanel Fixed EffectsPermutation TestRobust Regression
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