lmrob {robustbase} | R Documentation |
Computes fast MM-type estimators for linear (regression) models.
lmrob(formula, data, subset, weights, na.action, method = "MM", model = TRUE, x = !control$compute.rd, y = FALSE, singular.ok = TRUE, contrasts = NULL, offset = NULL, control = NULL, ...)
formula |
a symbolic description of the model to be fit. See
|
data |
an optional data frame, list or environment (or object
coercible by |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
weights |
an optional vector of weights to be used in the fitting process. |
na.action |
a function which indicates what should happen
when the data contain |
method |
string specifying the estimator-chain. |
model, x, y |
logicals. If |
singular.ok |
logical. If |
contrasts |
an optional list. See the |
offset |
this can be used to specify an a priori
known component to be included in the linear predictor
during fitting. An |
control |
a |
... |
can be used to specify control parameters directly
instead of via |
This function computes an MM-type regression estimator
as described in Yohai (1987) and Koller and Stahel (2011). By default
it uses a bi-square re-desceding score function, and it returns a
highly robust and highly efficient estimator (with 50% breakdown
point and 95% asymptotic efficiency for normal errors). The
computation is carried out by a call to lmrob.fit()
.
The argument setting
of lmrob.control
is provided
to set alternative defaults as suggested in Koller and Stahel (2011)
(use setting='KS2011'
). For details, see
lmrob.control
.
As initial estimator it uses an S-estimator (Rousseeuw and Yohai,
1984) which is computed using the Fast-S algorithm of Salibian-Barrera
and Yohai (2006), calling the function lmrob.S
. The
following chain of estimates is customizable via the method
argument of lmrob.control
. There are currently two types
of estimates available: M
and D
. The first corresponds
to the standard M-regression estimate. D
stands for the Design
Adaptive Scale estimate as proposed in Koller and Stahel (2011). The
method
argument takes a string that specifies the estimates to
be calculated as a chain. Setting method='SMDM'
will result in
an intial S-estimate, followed by an M-estimate, a Design Adaptive
Scale estimate and a final M-step. For methods involving a
D
-step, the default psi value of psi is changed to lqq
.
By default, standard errors are computed using the formulas of Croux,
Dhaene and Hoorelbeke (2003) (lmrob.control
option
cov=".vcov.avar1"
). This method, however, works only for
MM-estimates. For other method
arguments, the covariance matrix
estimate used is based on the asymptotic normality of the estimated
coefficients (cov=".vcov.w"
) as described in Koller and Stahel
(2011).
An object of class lmrob
. A list that includes the
following components:
coefficients |
The estimate of the coefficient vector |
init.S |
The list returned by |
init |
A similar list that contains the results of intermediate estimates (not for MM-estimates). |
scale |
The scale as used in the M estimator. |
cov |
The estimated covariance matrix of the regression coefficients |
residuals |
Residuals associated with the estimator |
fitted.values |
Fitted values associated with the estimator |
weights |
the “robustness weights” ψ(r_i/S) / (r_i/S). |
converged |
|
Matias Salibian-Barrera and Manuel Koller
Croux, C., Dhaene, G. and Hoorelbeke, D. (2003) Robust standard errors for robust estimators, Discussion Papers Series 03.16, K.U. Leuven, CES.
Koller, M. and Stahel, W.A. (2011), Sharpening Wald-type inference in robust regression for small samples, Computational Statistics & Data Analysis 55(8), 2504–2515.
Rousseeuw, P.J. and Yohai, V.J. (1984) Robust regression by means of S-estimators, In Robust and Nonlinear Time Series, J. Franke, W. H\"ardle and R. D. Martin (eds.). Lectures Notes in Statistics 26, 256–272, Springer Verlag, New York.
Salibian-Barrera, M. and Yohai, V.J. (2006) A fast algorithm for S-regression estimates, Journal of Computational and Graphical Statistics, 15(2), 414–427.
Yohai, V.J. (1987) High breakdown-point and high efficiency estimates for regression. The Annals of Statistics 15, 642–65.
lmrob.control
;
for the algorithms lmrob.S
and lmrob.fit
;
and for methods,
predict.lmrob
, summary.lmrob
,
print.lmrob
, and plot.lmrob
.
lmrob..M..fit
for examples on how to use a custom
initial estimate.
data(coleman) summary( m1 <- lmrob(Y ~ ., data=coleman) ) summary( m2 <- lmrob(Y ~ ., data=coleman, setting = 'KS2011') ) data(starsCYG, package = "robustbase") ## Plot simple data and fitted lines plot(starsCYG) lmST <- lm(log.light ~ log.Te, data = starsCYG) (RlmST <- lmrob(log.light ~ log.Te, data = starsCYG)) abline(lmST, col = "red") abline(RlmST, col = "blue") summary(RlmST) vcov(RlmST) stopifnot(all.equal(fitted(RlmST), predict(RlmST, newdata = starsCYG), tol = 1e-14))