FRBmultiregGS {FRB} | R Documentation |
Computes GS-estimates for multivariate regression together with standard errors, confidence intervals and p-values based on the Fast and Robust Bootstrap.
## S3 method for class 'formula': FRBmultiregGS(formula, data, ...) ## Default S3 method: FRBmultiregGS(X, Y, R = 999, bdp = 0.5, conf = 0.95, control=GScontrol(...), ...)
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. |
R |
number of bootstrap samples. |
bdp |
required breakdown point. Should have 0 < bdp <= 0.5, the default is 0.5. |
conf |
confidence level of the bootstrap confidence intervals. Default is conf=0.95 . |
control |
a list with control parameters for tuning the computing algorithm, see GScontrol (). |
... |
allows for specifying control parameters directly instead of via control . |
Generalized S-estimators are defined by minimizing the determinant of a robust estimator of the scatter matrix of
the differences of the residuals. Hence, this procedure is intercept free and only gives an estimate for the slope matrix. To estimate
the intercept, we use the M-type estimator of location of Lopuhaa (1992) on the residuals with the residual scatter matrix
estimate of the residuals as a preliminary estimate. This computation is carried out by a call to GSest_multireg
(),
which uses a fast-S-type algorithm (its tuning parameters can be changed via the control
argument).
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 (BCa)
confidence intervals (Davison and Hinkley 1997, p.194 and p.204 respectively).
Apart from the intervals with the requested confidence level, the function also returns p-values for each coefficient
corresponding to the hypothesis that the actual coefficient is zero. The p-values are computed as
1 minus the smallest level for which the confidence intervals would include zero. Both BCa and basic bootstrap p-values in this sense are given.
The bootstrap calculation is carried out by a call to GSboot_multireg
(), the result
of which is returned as the value bootest
. Bootstrap standard errors are returned as well.
Note: Bootstrap samples which contain too few distinct observations with positive weights are discarded
(a warning is given if this happens). The number of samples actually used is returned via ROK
.
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.
An object of class FRBmultireg
, which is a list containing the following components:
Beta |
GS-estimate for slope |
intercept |
estimate for the intercept |
Sigma |
GS-estimate for the error covariance matrix |
SE |
bootstrap standard errors corresponding to the elements in Beta |
CI.bca.lower |
a matrix containing the lower bound of the bias corrected and accelerated confidence intervals for each element of Beta |
CI.bca.upper |
a matrix containing the upper bound of the bias corrected and accelerated confidence intervals for each element of Beta |
CI.basic.lower |
a matrix containing the lower bound of basic bootstrap intervals for each element of Beta |
CI.basic.upper |
a matrix containing the upper bound of basic bootstrap intervals for each element of Beta |
p.bca |
a matrix containing the p-values based on the BCa confidence intervals for each element in Beta . |
p.basic |
a matrix containing the p-values based on the basic bootstrap intervals for each element in Beta . |
est |
GS-estimates as returned by the call to GSest_multireg () |
bootest |
bootstrap results for the GS-estimates as returned by the call to GSboot_multireg () |
conf |
a copy of the conf argument |
method |
a list with following components: est = character string indicating that GS-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 |
ROK |
number of bootstrap samples actually used (i.e. not discarded due to too few distinct observations with positive weight) |
w |
implicit weights corresponding to the GS-estimates (i.e. final weights in the RWLS procedure for the intercept estimate) |
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 |
Ella Roelant and Gert Willems
summary.FRBmultireg
, print.FRBmultireg
, plot.FRBmultireg
, GSboot_multireg
, GSest_multireg
,
FRBmultiregMM
, FRBmultiregS
, GScontrol
data(schooldata) school.x <- data.matrix(schooldata[,1:5]) school.y <- data.matrix(schooldata[,6:8]) #computes 25% breakdown point GS-estimate and 99% confidence intervals #based on 999 bootstrap samples: GSres <- FRBmultiregGS(school.x, school.y, R=999, bdp = 0.25, conf = 0.99) #or, equivalently, GSres <- FRBmultiregGS(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 GSres #the summary function additionally displays the confidence intervals and p-values #("BCA" method by default) summary(GSres) summary(GSres, confmethod="basic") #ask explicitely for the coefficient matrix: GSres$Beta #or for the error covariance matrix: GSres$Sigma #plot some bootstrap histograms for the coefficient estimates #(with "BCA" intervals by default) plot(GSres, which=2, expl=c("education", "occupation"), resp=c("selfesteem","reading")) #plot bootstrap histograms for all coefficient estimates plot(GSres, which=2) #possibly the plot-function has made a selection of coefficients to plot here, #since 'all' may have been too many to fit on one page, see help(plot.FRBmultireg); #this is platform-dependent # diagnostic plot for outlier detection: plot(GSres, which=1) # this may take a while, since the function needs to compute GS-estimates # for the X matrix