Robust Statistical Methods
Robust (or "resistant") methods for statistics modelling have been available in S from the very beginning in the 1980s; and then in R in package
stats. Examples are
mean(*, trim = . ),
IQR(), or also
fivenum(), the statistic behind
boxplot() in package
loess()) for robust nonparametric regression, which had been complemented by
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 Modern Applied Statistics with S). Most importantly, they provide
rlm() for robust regression and
cov.rob() for 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.
lmRob()(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). The
lmrob.S()functions are available in robustbase, but rather for comparison purposes.
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 splines. 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
mblm()fits median-based (Theil-Sen or Siegel's repeated) simple linear models. Package TEEReg provides trimmed elemental estimators for linear models. Generalized linear models (GLMs) are provided both via
glmRob()(robust), where package robustloggamma focuses on generalized log gamma models. Robust ordinal regression is provided by rorutadis (UTADIS). Robust Nonlinear model fitting is available through robustbase's
nlrob(). 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.
Depends") 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") and rospca. Historically, note that robust PCA can be performed by using standard R's
X <- stackloss; pc.rob <- princomp(X, covmat= MASS::cov.rob(X))Here, robustbase contains a slightly more flexible version,
fastmcd(), and similarly for
covOGK(). OTOH, robust's
covRob()has automatically chosen methods, notably
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 K-means Clustering. 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, particularly on
FastQn(). covRobust provides the nearest neighbor variance estimation (NNVE) method of Wang and Raftery (2002).
pam()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 genie, Gmedian, 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 Multivariate and Cluster
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.)
boxplot.stats(), etc mentioned above
runmed()provides most robust running median filtering.
vcov(lmrob())also uses a version of HAC standard errors for its robustly estimated linear models. See also the CRAN task view Econometrics
7 months ago