FRBmultiregS {FRB} | R Documentation |
Computes S-estimates for multivariate regression together with standard errors and confidence intervals based on the Fast and Robust Bootstrap.
## S3 method for class 'formula': FRBmultiregS(formula, data, ...) ## Default S3 method: FRBmultiregS(X, Y, int = TRUE, R = 999, bdp = 0.5, conf = 0.95, control=Scontrol(...), ...)
formula |
an object of class formula ; a symbolic description of the model to be fit. |
data |
data frame from which variables specified in formula are to be taken. |
X |
a matrix or data frame containing the explanatory variables. |
Y |
a matrix or data frame containing the response variables. |
int |
logical: if TRUE an intercept term is added to the model (unless it is already present in X ) |
R |
number of bootstrap samples |
bdp |
required breakdown point for the S-estimates. Should have 0 < bdp <= 0.5, the default is 0.5 |
conf |
level of the bootstrap confidence intervals. Default is conf=0.95 |
control |
a list with control parameters for tuning the computing algorithm, see Scontrol (). |
... |
allows for specifying control parameters directly instead of via control |
Multivariate S-estimates were introduced by Davies (1987) and can be highly robust while enjoying a reasonable Gaussian efficiency.
Their use in the multivariate regression setting was discussed in Van Aelst and Willems (2005).
The loss function used here is Tukey's biweight. It is tuned in order to achieve the required breakdown point bdp
(any value between 0 and 0.5).
The computation is carried out by a call to Sest_multireg
(), which performs the fast-S algorithm
(Salibian-Barrera and Yohai 2006), see Scontrol
for its tuning parameters.
The result of this call is also returned as the value est
.
The Fast and Robust Bootstrap (Salibian-Barrera and Zamar 2002) is used to calculate so-called
basic bootstrap confidence intervals and bias corrected and accelerated
confidence intervals (Davison and Hinkley 1997, p.194 and p.204 respectively). This computation is carried out by a call to Sboot_multireg
(), the result
of which is returned as the value bootest
. Bootstrap standard errors are returned as well.
In the formula
-interface, a multivariate response is produced via cbind
. For example cbind(x4,x5) ~ x1+x2+x3
.
All arguments from the default method can also be passed to the formula
method except for int
(passing int
explicitely
will produce an error; the inclusion of an intercept term is determined by formula
).
An object of class FRBmultireg
, which is a list containing the following components:
Beta |
S-estimate for the regression coefficients |
Sigma |
S-estimate for the error covariance matrix |
SE |
bootstrap standard errors corresponding to the elements in Beta |
CI.bca.lower |
a matrix containing the lower bounds of the bias corrected and accelerated confidence intervals for each element in Beta . |
CI.bca.upper |
a matrix containing the upper bounds of the bias corrected and accelerated confidence intervals for each element in Beta . |
CI.basic.lower |
a matrix containing the lower bounds of basic bootstrap intervals for each element in Beta . |
CI.basic.upper |
a matrix containing the upper bounds of basic bootstrap intervals for each element in Beta . |
est |
S-estimates as returned by the call to Sest_multireg () |
bootest |
bootstrap results for the S-estimates as returned by the call to Sboot_multireg () |
conf |
a copy of the conf argument |
method |
a list with following components: est = character string indicating that S-estimates were used, and
bdp = a copy of the bdp argument |
control |
a copy of the control argument |
X, Y |
either copies of the respective arguments or the corresponding matrices produced from formula |
Gert Willems and Ella Roelant
summary.FRBmultireg
, print.FRBmultireg
, plot.FRBmultireg
, Sboot_multireg
,
Sest_multireg
, FRBmultiregMM
, FRBmultiregGS
, Scontrol
data(schooldata) school.x <- data.matrix(schooldata[,1:5]) school.y <- data.matrix(schooldata[,6:8]) #computes 25% breakdown point S-estimate and 99% confidence intervals #based on 999 bootstrap samples: Sres <- FRBmultiregS(school.x, school.y, R=999, bdp = 0.25, conf = 0.99) #or, equivalently, Sres <- FRBmultiregS(cbind(reading,mathematics,selfesteem)~., data=schooldata, R=999, bdp = 0.25, conf = 0.99) #the print method displays the coefficients with their bootstrap standard errors Sres #the summary function additionally displays the confidence intervals #("BCA" method by default) summary(Sres) summary(Sres, confmethod="basic") #ask explicitely for the coefficient matrix: Sres$Beta #or for the error covariance matrix: Sres$Sigma #plot some bootstrap histograms for the coefficient estimates #(with "BCA" intervals by default) plot(Sres, which=2, expl=c("education", "occupation"), resp=c("selfesteem","reading")) #plot bootstrap histograms for all coefficient estimates plot(Sres, which=2) #probably the plot-function has made a selection of coefficients to plot here, #since 'all' was too many to fit on one page, see help(plot.FRBmultireg); #this is platform-dependent # diagnostic plot for outlier detection: plot(Sres, which=1) # this may take a while, since the function needs to compute S-estimates # for the X matrix