# Plots of the Output of a Bootstrap Simulation This takes a bootstrap object and produces plots for the bootstrap replicates of the variable of interest. ```r ## S3 method for class 'boot' plot(x, index = 1, t0 = NULL, t = NULL, jack = FALSE, qdist = "norm", nclass = NULL, df, ...) ``` ## Arguments - `x`: An object of class `"boot"` returned from one of the bootstrap generation functions. - `index`: The index of the variable of interest within the output of `boot.out`. This is ignored if `t` and `t0` are supplied. - `t0`: The original value of the statistic. This defaults to `boot.out$t0[index]` unless `t` is supplied when it defaults to `NULL`. In that case no vertical line is drawn on the histogram. - `t`: The bootstrap replicates of the statistic. Usually this will take on its default value of `boot.out$t[,index]`, however it may be useful sometimes to supply a different set of values which are a function of `boot.out$t`. - `jack`: A logical value indicating whether a jackknife-after-bootstrap plot is required. The default is not to produce such a plot. - `qdist`: The distribution against which the Q-Q plot should be drawn. At present `"norm"` (normal distribution - the default) and `"chisq"` (chi-squared distribution) are the only possible values. - `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 `ceiling(length(t)/25)`. - `df`: If `qdist` is `"chisq"` then this is the degrees of freedom for the chi-squared distribution to be used. It is a required argument in that case. - `...`: When `jack` is `TRUE` additional parameters to `jack.after.boot` can be supplied. See the help file for `jack.after.boot` for details of the possible parameters. ## Returns `boot.out` is returned invisibly. ## 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 `t0` is at a breakpoint and all intervals are of equal length. A vertical dotted line indicates the position of `t0`. This cannot be done if `t` is supplied but `t0` is not and so, in that case, the breakpoints are computed by `hist` using the `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 `mean(t)` and slope `sqrt(var(t))` while for the chi-squared it has intercept 0 and slope 1. If `jack` is `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 `jack.after.boot` for further details of this plot. ## See Also `boot`, `jack.after.boot`, `print.boot` ## Examples ```r # 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) ```

plot.boot function