Robust (or "resistant") methods for statistics modelling have been
available in S from the very beginning in the 1980s; and then in R in
mean(*, trim =
fivenum(), the statistic
boxplot() in package
loess()) for robust
nonparametric regression, which had been complemented
runmed() in 2003.
Much further important functionality has been made available in
recommended (and hence present in all R versions) package
MASS (by Bill Venables and Brian Ripley, see the book
Statistics with S).
Most importantly, they provide
rlm() for robust regression and
robust multivariate scatter and covariance.
This task view is about R add-on packages providing newer or faster,
more efficient algorithms and notably for (robustification of) new models.
Please send suggestions for additions and extensions to the
task view maintainer.
An international group of scientists working in the field of robust
statistics has made efforts (since October 2005) to coordinate several of
the scattered developments and make the important ones available
through a set of R packages complementing each other.
These should build on a basic package with "Essentials",
coined robustbase with (potentially many) other packages
building on top and extending the essential functionality to particular
models or applications.
Further, there is the quite comprehensive package
robust, a version of the robust library of S-PLUS,
as an R package now GPLicensed thanks to Insightful and Kjell Konis.
Originally, there has been much overlap between 'robustbase'
and 'robust', now robust depends
on robustbase, the former providing convenient routines for
the casual user where the latter will contain the underlying
functionality, and provide the more advanced statistician with a
large range of options for robust modeling.
We structure the packages roughly into the following topics, and
typically will first mention functionality in packages
robustbase and robust.
- Regression (Linear, Generalized Linear, Nonlinear Models,
incl. Mixed Effects):
lmrob() (robustbase) and
(robust) where the former uses the latest of the
fast-S algorithms and heteroscedasticity and autocorrelation corrected
(HAC) standard errors, the latter makes use of the M-S algorithm of
Maronna and Yohai (2000), automatically when there are factors
among the predictors (where S-estimators (and hence MM-estimators)
based on resampling typically badly fail).
are available in robustbase, but rather for comparison
rlm() from MASS had been the first widely
available implementation for robust linear models, and also one of
the very first MM-estimation implementations.
robustreg provides very simple M-estimates for linear
regression (in pure R).
Note that Koenker's quantile regression package quantreg
contains L1 (aka LAD, least absolute deviations)-regression as a
special case, doing so also for nonparametric regression via
Quantile regression (and hence L1 or LAD) for mixed effect models,
is available in package lqmm, whereas an
MM-like approach for robust linear mixed effects modeling
is available from package robustlmm.
Package mblm's function
median-based (Theil-Sen or Siegel's repeated) simple linear models.
Package TEEReg provides trimmed elemental estimators for
Generalized linear models (GLMs) are provided both via
glmrob() (robustbase) and
where package robustloggamma focuses on generalized log
Robust ordinal regression is provided by
Robust Nonlinear model fitting is available through
multinomRob fits overdispersed multinomial regression
models for count data.
rgam and robustgam both fit robust GAMs,
i.e., robust Generalized Additive Models.
drgee fits "Doubly Robust" Generalized Estimating Equations (GEEs)
complmrob does robust linear regression with compositional data as covariates.
- Multivariate Analysis:
Here, the rrcov package which builds ("
on robustbase provides nice S4 class based methods,
more methods for robust multivariate variance-covariance estimation,
and adds robust PCA methodology.
It is extended by rrcovNA, providing robust multivariate
methods for for incomplete or missing (
NA) data, and by
rrcovHD, providing robust multivariate methods for
High Dimensional data. High dimensional data with an
emphasis on functional data are treated robustly also by roahd.
Specialized robust PCA packages are pcaPP (via
Projection Pursuit), rpca (incl "sparse")
Historically, note that robust PCA can be performed by using standard
X <- stackloss; pc.rob <- princomp(X, covmat= MASS::cov.rob(X))
Here, robustbase contains a slightly more flexible
covMcd() than robust's
fastmcd(), and similarly for
covRob() has automatically chosen
pairwiseQC() for large dimensionality p.
Package robustX for experimental, or other not yet
established procedures, contains
covNCC(), the latter providing the
neighbor variance estimation (NNVE) method of Wang and Raftery (2002),
also available (slightly less optimized) in covRobust.
RobRSVD provides a robust Regularized Singular Value Decomposition.
mvoutlier (building on robustbase) provides
several methods for outlier identification in high dimensions.
GSE estimates multivariate location and scatter in the presence of missing data.
RSKC provides Robust Sparse
robustDA for robust mixture Discriminant Analysis
(RMDA) builds a mixture model classifier with noisy class labels.
robcor computes robust pairwise correlations based on scale estimates,
covRobust provides the
nearest neighbor variance estimation (NNVE) method of Wang and
- Clustering (Multivariate):
We are not considering cluster-resistant variance (/standard error)
estimation (aka "sandwich"). Rather e.g. model based
and hierarchical clustering methodology with a particular emphasis
on robustness: Note that cluster's
implementing "partioning around medians" is partly robust (medians
instead of very unrobust k-means) but is not good enough,
as e.g., the k clusters could consist of k-1 outliers one
cluster for the bulk of the remaining data.
"Truly" robust clustering is provided by packages
otrimle (trimmed MLE model-based)
snipEM, (snipping EM)
and qclust (robust estim. of Gaussian mixtures) and
notably tclust (robust trimmed clustering).
See also the CRAN task views
- Large Data Sets:
BACON() (in robustX)
should be applicable for larger (n,p) than traditional robust
covariance based outlier detectors.
OutlierDM detects outliers for replicated high-throughput data.
(See also the CRAN task view MachineLearning.)
- Descriptive Statistics / Exploratory Data Analysis:
boxplot.stats(), etc mentioned above
- Time Series:
Note however that these (last two items) are not yet available from CRAN.
runmed() provides most robust
running median filtering.
Package robfilter contains robust regression and
filtering methods for univariate time series, typically based on
repeated (weighted) median regressions.
The RobPer provides several methods for robust
periodogram estimation, notably for irregularly spaced time series.
Peter Ruckdeschel has started to lead an effort for a robust
time-series package, see robust-ts on R-Forge.
Further, robKalman, "Routines for Robust Kalman
Filtering --- the ACM- and rLS-filter", is being developed, see
robkalman on R-Forge.
- Econometric Models:
Econometricians tend to like HAC (heteroscedasticity and
autocorrelation corrected) standard errors. For a broad class of
models, these are provided by package sandwich.
vcov(lmrob()) also uses a version of HAC
standard errors for its robustly estimated linear models.
See also the CRAN task view Econometrics
- Robust Methods for Bioinformatics:
There are several packages in the Bioconductor project
providing specialized robust methods.
In addition, RobLoxBioC provides infinitesimally robust
estimators for preprocessing omics data.
- Robust Methods for Survival Analysis:
Package coxrobust provides robust estimation in the Cox
OutlierDC detects outliers using quantile regression for
- Robust Methods for Surveys:
On R-forge only, package rhte provides a robust
Package georob aims at robust geostatistical
analysis of spatial data, such as kriging and more.
- Collections of several methodologies:
- WRS2 contains
robust tests for ANOVA and ANCOVA and other functionality from
Rand Wilcox's collection.
- walrus builds on WRS2's computations,
providing a different user interface.
- robeth contains R functions interfacing to the extensive
RobETH fortran library with many functions for regression,
multivariate estimation and more.
- Other approaches to robust and resistant methodology:
The package distr and its several child packages
also allow to explore robust estimation concepts, see e.g.,
distr on R-Forge.
Notably, based on these,
the project robast aims for the implementation of R
packages for the computation of optimally robust estimators and
tests as well as the necessary infrastructure (mainly S4 classes
and methods) and diagnostics; cf. M. Kohl (2005).
It includes the R packages
RandVar, RobAStBase, RobLox,
Further, ROptEst, and ROptRegTS.
- RobustAFT computes Robust Accelerated Failure
Time Regression for Gaussian and logWeibull errors.
- robumeta for robust variance meta-regression;
metaplus adds robustness via t- or mixtures of
- ssmrob provides robust estimation and inference in sample selection models.