Description Usage Arguments Details Value Author(s) References See Also Examples
View source: R/Sest_multireg.R
Computes S-Estimates of multivariate regression based on Tukey's biweight function using the fast-S algorithm.
1 2 3 4 5 6 |
formula |
an object of class |
data |
data frame from which variables specified in formula are to be taken. |
X |
a matrix or data frame containing the explanatory variables (possibly including intercept). |
Y |
a matrix or data frame containing the response variables. |
int |
logical: if |
bdp |
required breakdown point. Should have 0 < |
control |
a list with control parameters for tuning the computing algorithm, see |
na.action |
a function which indicates what should happen when the data contain NAs. Defaults to |
... |
allows for specifying control parameters directly instead of via |
This function is called by FRBmultiregS
.
S-estimates for multivariate regression were discussed in Van Aelst and Willems (2005). The algorithm used here is a multivariate
version of the fast-S algorithm introduced by Salibian-Barrera and Yohai (2006).
See Scontrol
for the adjustable tuning parameters of this algorithm.
Apart from the regression coefficients, the function returns both the error covariance matrix estimate Sigma
and
the corresponding shape estimate Gamma
(which has determinant equal to 1).
The scale
is determined by det(Sigma)^{1/2/q}, with q the number of response variables.
The returned object inherits from class mlm
such that the standard coef
, residuals
, fitted
and predict
functions can be used.
An object of class FRBmultireg
which extends class mlm
and contains at least the following components:
coefficients |
S-estimates of the regression coefficients |
residuals |
the residuals, that is response minus fitted values |
fitted.values |
the fitted values. |
Gamma |
S-estimate of the error shape matrix |
Sigma |
S-estimate of the error covariance matrix |
scale |
S-estimate of the size of the multivariate errors |
weights |
implicit weights corresponding to the S-estimates (i.e. final weights in the RWLS procedure at the end of the fast-S algorithm) |
outFlag |
outlier flags: 1 if the robust distance of the residual exceeds the .975 quantile of (the square root of) the chi-square distribution with degrees of freedom equal to the dimension of the responses; 0 otherwise |
b,c |
tuning parameters used in Tukey biweight loss function, as determined by |
method |
a list with following components: |
control |
a copy of the |
Gert Willems, Stefan Van Aelst and Ella Roelant
M. Salibian-Barrera and V. Yohai (2006) A fast algorithm for S-regression estimates. Journal of Computational and Graphical Statistics, 15, 414–427.
S. Van Aelst and G. Willems (2005) Multivariate regression S-estimators for robust estimation and inference. Statistica Sinica, 15, 981–1001
S. Van Aelst and G. Willems (2013). Fast and robust bootstrap for multivariate inference: The R package FRB. Journal of Statistical Software, 53(3), 1–32. URL: http://www.jstatsoft.org/v53/i03/.
FRBmultiregS
, Sboot_multireg
, MMest_multireg
, Scontrol
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | data(schooldata)
school.x <- data.matrix(schooldata[,1:5])
school.y <- data.matrix(schooldata[,6:8])
# compute 25% breakdown S-estimates
Sres <- Sest_multireg(school.x,school.y, bdp=0.25)
# or using the formula interface
Sres <- Sest_multireg(cbind(reading,mathematics,selfesteem)~., data=schooldata, bdp=0.25)
# the regression coefficients:
Sres$coefficients
# or alternatively
coef(Sres)
n <- nrow(schooldata)
par(mfrow=c(2,1))
# the estimates can be considered as weighted least squares estimates with the
# following implicit weights
plot(1:n, Sres$weights)
# Sres$outFlag tells which points are outliers based on whether or not their
# robust distance exceeds the .975 chi-square cut-off:
plot(1:n, Sres$outFlag)
# (see also the diagnostic plot in plotDiag())
|
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