| jack.after.boot {boot} | R Documentation |
This function calculates the jackknife influence values from a bootstrap output object and plots the corresponding jackknife-after-bootstrap plot.
jack.after.boot(boot.out, index=1, t=NULL, L=NULL, useJ=TRUE,
stinf=TRUE, alpha=NULL, main="", ylab=NULL, ...)
boot.out |
An object of class "boot" which would normally be created by a call
to boot. It should represent a nonparametric bootstrap.
For reliable results boot.out$R should be reasonably large.
|
index |
The index of the statistic of interest in the output of boot.out$statistic.
|
t |
A vector of length boot.out$R giving the bootstrap replicates of the statistic
of interest. This is useful if the statistic of interest is a function of
the calculated bootstrap output. If it is not supplied then the default is
boot.out$t[,index].
|
L |
The empirical influence values for the statistic of interest. These are used
only if useJ is FALSE. If they are not supplied and are needed, they are
calculated by a call to empinf. If L is supplied then it is assumed that
they are the infinitesimal jackknife values.
|
useJ |
A logical variable indicating if the jackknife influence values calculated from
the bootstrap replicates should be used. If FALSE the empirical influence
values are used. The default is TRUE.
|
stinf |
A logical variable indicating whether to standardize the jackknife values
before plotting them. If TRUE then the jackknife values used are divided by
their standard error.
|
alpha |
The quantiles at which the plots are required. The default is
c(0.05, 0.1, 0.16, 0.5, 0.84, 0.9, 0.95).
|
main |
A character string giving the main title for the plot. |
ylab |
The label for the Y axis. If the default values of alpha are used and ylab
is not supplied then a label indicating which percentiles are plotted is used.
If alpha is supplied then the default label will not say which percentiles
were used.
|
... |
Any extra arguments required by boot.out$statistic. These are required only
if useJ is FALSE and L is not supplied, in which case they are passed to
empinf for use in calculation of the empirical influence values.
|
The centred jackknife quantiles for each observation are estimated from those
bootstrap samples in which the particular observation did not appear. These
are then plotted against the influence values. If useJ is TRUE then the
influence values are found in the same way as the difference between the
mean of the statistic in the samples excluding the observations and the mean in
all samples. If useJ is FALSE then empirical influence values are
calculated by calling empinf.
The resulting plots are useful diagnostic tools for looking at the way individual observations affect the bootstrap output.
The plot will consist of a number of horizontal dotted lines which correspond to the quantiles of the centred bootstrap distribution. For each data point the quantiles of the bootstrap distribution calculated by omitting that point are plotted against the (possibly standardized) jackknife values. The observation number is printed below the plots. To make it easier to see the effect of omitting points on quantiles, the plotted quantiles are joined by line segments. These plots provide a useful diagnostic tool in establishing the effect of individual observations on the bootstrap distribution. See the references below for some guidelines on the interpretation of the plots.
There is no returned value but a plot is generated on the current graphics display.
A plot is created on the current graphics device.
Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.
Efron, B. (1992) Jackknife-after-bootstrap standard errors and influence functions (with Discussion). Journal of the Royal Statistical Society, B, 54, 83–127.
# To draw the jackknife-after-bootstrap plot for the head size data as in
# Example 3.24 of Davison and Hinkley (1997)
pcorr <- function( x )
{
# function to find the correlations and partial correlations between
# the four measurements.
v <- cor(x)
v.d <- diag(var(x))
iv <- solve(v)
iv.d <- sqrt(diag(iv))
iv <- - diag(1/iv.d) %*% iv %*% diag(1/iv.d)
q <- NULL
n <- nrow(v)
for (i in 1:(n-1))
q <- rbind( q, c(v[i,1:i],iv[i,(i+1):n]) )
q <- rbind( q, v[n,] )
diag(q) <- round(diag(q))
q
}
frets.fun <- function( data, i )
{ d <- data[i,]
v <- pcorr( d )
c(v[1,],v[2,],v[3,],v[4,])
}
frets.boot <- boot(log(as.matrix(frets)), frets.fun, R=999)
# we will concentrate on the partial correlation between head breadth
# for the first son and head length for the second. This is the 7th
# element in the output of frets.fun so we set index=7
jack.after.boot(frets.boot,useJ=FALSE,stinf=FALSE,index=7)