FRBmultiregGS {FRB}R Documentation

GS-Estimates for multivariate regression with bootstrap confidence intervals

Description

Computes GS-estimates for multivariate regression together with standard errors and confidence intervals based on the Fast and Robust Bootstrap.

Usage

## S3 method for class 'formula':
FRBmultiregGS(formula, data, ...)

## Default S3 method:
FRBmultiregGS(X, Y, R = 999, bdp = 0.5, conf = 0.95, 
                control=GScontrol(...), ...)

Arguments

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.

Details

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 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 GSboot_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.

Value

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
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

Author(s)

Ella Roelant and Gert Willems

References

See Also

summary.FRBmultireg, print.FRBmultireg, plot.FRBmultireg, GSboot_multireg, GSest_multireg, FRBmultiregMM, FRBmultiregS, GScontrol

Examples

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 
#("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

[Package FRB version 1.4 Index]