Robustly sequence candidate predictors according to their predictive content and find the optimal model along the sequence.
rlars(x, ...)# S3 method for formula
rlars(formula, data, ...)
# S3 method for default
rlars(x, y, sMax = NA, centerFun = median,
scaleFun = mad, winsorize = FALSE, const = 2, prob = 0.95,
fit = TRUE, s = c(0, sMax), regFun = lmrob, regArgs = list(),
crit = c("BIC", "PE"), splits = foldControl(), cost = rtmspe,
costArgs = list(), selectBest = c("hastie", "min"), seFactor = 1,
ncores = 1, cl = NULL, seed = NULL, model = TRUE,
tol = .Machine$double.eps^0.5, ...)
a matrix or data frame containing the candidate predictors.
additional arguments to be passed down. For the default
method, additional arguments to be passed down to
robStandardize.
a formula describing the full model.
an optional data frame, list or environment (or object coercible
to a data frame by as.data.frame) containing the variables in
the model. If not found in data, the variables are taken from
environment(formula), typically the environment from which
rlars is called.
a numeric vector containing the response.
an integer giving the number of predictors to be sequenced. If
it is NA (the default), predictors are sequenced as long as there are
twice as many observations as predictors.
a function to compute a robust estimate for the center
(defaults to median).
a function to compute a robust estimate for the scale
(defaults to mad).
a logical indicating whether to clean the full data set by
multivariate winsorization, i.e., to perform data cleaning RLARS instead of
plug-in RLARS (defaults to FALSE).
numeric; tuning constant to be used in the initial corralation estimates based on adjusted univariate winsorization (defaults to 2).
numeric; probability for the quantile of the \(\chi^{2}\) distribution to be used in bivariate or multivariate winsorization (defaults to 0.95).
a logical indicating whether to fit submodels along the sequence
(TRUE, the default) or to simply return the sequence (FALSE).
an integer vector of length two giving the first and last step
along the sequence for which to compute submodels. The default is to start
with a model containing only an intercept (step 0) and iteratively add all
variables along the sequence (step sMax). If the second element is
NA, predictors are added to the model as long as there are twice
as many observations as predictors. If only one value is supplied, it is
recycled.
a function to compute robust linear regressions along the
sequence (defaults to lmrob).
a list of arguments to be passed to regFun.
a character string specifying the optimality criterion to be
used for selecting the final model. Possible values are "BIC" for
the Bayes information criterion and "PE" for resampling-based
prediction error estimation.
an object giving data splits to be used for prediction error
estimation (see perry).
a list of additional arguments to be passed to the
prediction loss function cost.
arguments specifying a criterion for selecting
the best model (see perrySelect). The default is to
use a one-standard-error rule.
a positive integer giving the number of processor cores to be
used for parallel computing (the default is 1 for no parallelization). If
this is set to NA, all available processor cores are used. For
fitting models along the sequence and for prediction error estimation,
parallel computing is implemented on the R level using package
parallel. Otherwise parallel computing for some of of the more
computer-intensive computations in the sequencing step is implemented on the
C++ level via OpenMP (http://openmp.org/).
a parallel cluster for parallel computing as generated by
makeCluster. This is preferred over ncores
for tasks that are parallelized on the R level, in which case ncores
is only used for tasks that are parallelized on the C++ level.
optional initial seed for the random number generator (see
.Random.seed). This is useful because many robust regression
functions (including lmrob) involve randomness,
or for prediction error estimation. On parallel R worker processes, random
number streams are used and the seed is set via
clusterSetRNGStream.
a logical indicating whether the model data should be included in the returned object.
a small positive numeric value. This is used in bivariate winsorization to determine whether the initial estimate from adjusted univariate winsorization is close to 1 in absolute value. In this case, bivariate winsorization would fail since the points form almost a straight line, and the initial estimate is returned.
If fit is FALSE, an integer vector containing the indices of
the sequenced predictors.
Else if crit is "PE", an object of class
"perrySeqModel" (inheriting from class "perrySelect",
see perrySelect). It contains information on the
prediction error criterion, and includes the final model as component
finalModel.
Otherwise an object of class "rlars" (inheriting from class
"seqModel") with the following components:
activean integer vector containing the indices of the sequenced predictors.
san integer vector containing the steps for which submodels along the sequence have been computed.
coefficientsa numeric matrix in which each column contains the regression coefficients of the corresponding submodel along the sequence.
fitted.valuesa numeric matrix in which each column contains the fitted values of the corresponding submodel along the sequence.
residualsa numeric matrix in which each column contains the residuals of the corresponding submodel along the sequence.
dfan integer vector containing the degrees of freedom of the submodels along the sequence (i.e., the number of estimated coefficients).
robusta logical indicating whether a robust fit was
computed (TRUE for "rlars" models).
scalea numeric vector giving the robust residual scale estimates for the submodels along the sequence.
critan object of class "bicSelect" containing the
BIC values and indicating the final model (only returned if argument
crit is "BIC" and argument s indicates more than one
step along the sequence).
muXa numeric vector containing the center estimates of the predictors.
sigmaXa numeric vector containing the scale estimates of the predictors.
muYnumeric; the center estimate of the response.
sigmaYnumeric; the scale estimate of the response.
xthe matrix of candidate predictors (if model is
TRUE).
ythe response (if model is TRUE).
wa numeric vector giving the data cleaning weights (if
winsorize is TRUE).
callthe matched function call.
Khan, J.A., Van Aelst, S. and Zamar, R.H. (2007) Robust linear model selection based on least angle regression. Journal of the American Statistical Association, 102(480), 1289--1299.
# NOT RUN {
## generate data
# example is not high-dimensional to keep computation time low
library("mvtnorm")
set.seed(1234) # for reproducibility
n <- 100 # number of observations
p <- 25 # number of variables
beta <- rep.int(c(1, 0), c(5, p-5)) # coefficients
sigma <- 0.5 # controls signal-to-noise ratio
epsilon <- 0.1 # contamination level
Sigma <- 0.5^t(sapply(1:p, function(i, j) abs(i-j), 1:p))
x <- rmvnorm(n, sigma=Sigma) # predictor matrix
e <- rnorm(n) # error terms
i <- 1:ceiling(epsilon*n) # observations to be contaminated
e[i] <- e[i] + 5 # vertical outliers
y <- c(x %*% beta + sigma * e) # response
x[i,] <- x[i,] + 5 # bad leverage points
## fit robust LARS model
rlars(x, y, sMax = 10)
# }
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