Robust Linear Mixed Effects Models

Implements the Robust Scoring Equations estimator to fit linear mixed effects models robustly. Robustness is achieved by modification of the scoring equations combined with the Design Adaptive Scale approach.

Robust linear mixed effects models

The R-package robustlmm provides functions for estimating linear mixed effects models in a robust way.

The main workhorse is the function rlmer; it is implemented as direct robust analogue of the popular lmer function of the lme4 package. The two functions have similar abilities and limitations. A wide range of data structures can be modeled: mixed effects models with hierarchical as well as complete or partially crossed random effects structures are possible. While the lmer function is optimized to handle large datasets efficiently, the computations employed in the rlmer function are more complex and for this reason also more expensive to compute. The two functions have the same limitations in the support of different random effect and residual error covariance structures. Both support only diagonal and unstructured random effect covariance structures.

The robustlmm package implements most of the analysis tool chain as is customary in R. The usual functions such as summary, coef, resid, etc. are provided as long as they are applicable for this type of models (see rlmerMod-class for a full list). The functions are designed to be as similar as possible to the ones in the lme4 package to make switching between the two packages easy.

Inference is supported via:

• vcov(fit) (linearised, the lme4-inherited default) and vcov(fit, type = "sandwich") (robust cluster sandwich; see ?vcov_sandwich).
• confint(fit) returns the closed-form Wald interval, optionally with vcov_type = "sandwich". confint(fit, method = "boot") and method = "BCa" delegate to the peer-reviewed confintROB package (Mason, Cantoni & Ghisletta 2021, 2024), which is in Suggests.
• anova(fit) for a per-term Wald table; anova(fit0, fit1) for nested model comparison (Wald restriction for fixed effects, parametric-bootstrap quasi-deviance for variance-component tests on the PSD-cone boundary).
• predict(fit, interval = "confidence" / "prediction") with confidence / prediction intervals.
• cooks.distance(fit) for per-observation joint influence on $(\hat\beta, \hat\sigma, \hat\theta)$; caseweightIF(fit) for the case-weight influence function.
• rlmer(formula, data, init = "ransac") for a high-breakdown RANSAC start, useful when redescending psi-functions risk a phony local minimum.

An empirical evaluation of the inference methods (CI coverage, Type-I, power, under contamination) lives in inst/simulationStudy/inferenceStudy_results/ on the development branch.

Installation

This R-package is available on CRAN. Install it directly in R with the command

install.packages("robustlmm")

This package requires lme4 version at least 2.0-1 and other packages. Make sure to install them as well.

You can also install the package directly from github:

install.packages("devtools") ## if not already installed
require(devtools)
install_github("kollerma/robustlmm")
require(robustlmm)