\name{plot.boot}
\alias{plot.boot}
\title{
Plots of the Output of a Bootstrap Simulation
}
\description{
This takes a bootstrap object and produces plots for the bootstrap
replicates of the variable of interest.  
}
\usage{
\method{plot}{boot}(x, index = 1, t0 = NULL, t = NULL, jack = FALSE,
     qdist = "norm", nclass = NULL, df, \dots)
}
\arguments{
  \item{x}{
    An object of class \code{"boot"} returned from one of the bootstrap
    generation functions. 
  }
  \item{index}{
    The index of the variable of interest within the output of
    \code{boot.out}.  This is ignored if \code{t} and \code{t0} are
    supplied. 
  }
  \item{t0}{
    The original value of the statistic.  This defaults to
    \code{boot.out$t0[index]} unless \code{t} is supplied when it
    defaults to \code{NULL}. In that case no vertical line is drawn on
    the histogram.
  }
  \item{t}{
    The bootstrap replicates of the statistic.  Usually this will take
    on its default value of \code{boot.out$t[,index]}, however it may be
    useful sometimes to supply a different set of values which are a
    function of \code{boot.out$t}.
  }
  \item{jack}{
    A logical value indicating whether a jackknife-after-bootstrap plot is 
    required.  The default is not to produce such a plot.
  }
  \item{qdist}{
    The distribution against which the Q-Q plot should be drawn.  At
    present \code{"norm"} (normal distribution - the default) and
    \code{"chisq"} (chi-squared distribution) are the only possible
    values.
  }
  \item{nclass}{
    An integer giving the number of classes to be used in the bootstrap
    histogram.  The default is the integer between 10 and 100 closest to
    \code{ceiling(length(t)/25)}.
  }
  \item{df}{
    If \code{qdist} is \code{"chisq"} then this is the degrees of
    freedom for the chi-squared distribution to be used.  It is a
    required argument in that case.
  }
  \item{...}{
    When \code{jack} is \code{TRUE} additional parameters to
    \code{jack.after.boot} can be supplied.  See the help file for
    \code{jack.after.boot} for details of the possible parameters.
  }
}

\value{
  \code{boot.out} is returned invisibly.
}

\section{Side Effects}{
  All screens are closed and cleared and a number of plots are produced
  on the current graphics device.  Screens are closed but not cleared at
  termination of this function.
}
\details{
  This function will generally produce two side-by-side plots.  The left
  plot will be a histogram of the bootstrap replicates.  Usually the
  breaks of the histogram will be chosen so that \code{t0} is at a
  breakpoint and all intervals are of equal length.  A vertical dotted
  line indicates the position of \code{t0}.  This cannot be done if
  \code{t} is supplied but \code{t0} is not and so, in that case, the
  breakpoints are computed by \code{hist} using the \code{nclass}
  argument and no vertical line is drawn.

  The second plot is a Q-Q plot of the bootstrap replicates.  The order
  statistics of the replicates can be plotted against normal or
  chi-squared quantiles.  In either case the expected line is also
  plotted.  For the normal, this will have intercept \code{mean(t)} and
  slope \code{sqrt(var(t))} while for the chi-squared it has intercept 0
  and slope 1.
  
  If \code{jack} is \code{TRUE} a third plot is produced beneath these
  two.  That plot is the jackknife-after-bootstrap plot.  This plot may
  only be requested when nonparametric simulation has been used.  See
  \code{jack.after.boot} for further details of this plot.  
}
\seealso{
  \code{\link{boot}}, \code{\link{jack.after.boot}}, \code{\link{print.boot}}
}
\examples{
# We fit an exponential model to the air-conditioning data and use
# that for a parametric bootstrap.  Then we look at plots of the
# resampled means.
air.rg <- function(data, mle) rexp(length(data), 1/mle)

air.boot <- boot(aircondit$hours, mean, R = 999, sim = "parametric",
                 ran.gen = air.rg, mle = mean(aircondit$hours))
plot(air.boot)

# In the difference of means example for the last two series of the 
# gravity data
grav1 <- gravity[as.numeric(gravity[, 2]) >= 7, ]
grav.fun <- function(dat, w) {
     strata <- tapply(dat[, 2], as.numeric(dat[, 2]))
     d <- dat[, 1]
     ns <- tabulate(strata)
     w <- w/tapply(w, strata, sum)[strata]
     mns <- as.vector(tapply(d * w, strata, sum)) # drop names
     mn2 <- tapply(d * d * w, strata, sum)
     s2hat <- sum((mn2 - mns^2)/ns)
     c(mns[2] - mns[1], s2hat)
}

grav.boot <- boot(grav1, grav.fun, R = 499, stype = "w", strata = grav1[, 2])
plot(grav.boot)
# now suppose we want to look at the studentized differences.
grav.z <- (grav.boot$t[, 1]-grav.boot$t0[1])/sqrt(grav.boot$t[, 2])
plot(grav.boot, t = grav.z, t0 = 0)

# In this example we look at the one of the partial correlations for the
# head dimensions in the dataset frets.
frets.fun <- function(data, i) {
    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
    }
    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)
plot(frets.boot, index = 7, jack = TRUE, stinf = FALSE, useJ = FALSE)
}
\keyword{hplot}
\keyword{nonparametric}