Calculate one or multiple bootstrap confidence intervals

Calculate one or multiple bootstrap confidence intervals, given a sample of bootstrap replications.

Usage

bootstrap_CIs(
  boot_est,
  boot_se = NULL,
  est = NULL,
  se = NULL,
  CI_type = "percentile",
  level = 0.95,
  B_vals = length(boot_est),
  reps = 1L,
  format = "wide",
  seed = NULL
)

Arguments

boot_est: vector of bootstrap replications of an estimator.
boot_se: vector of estimated standard errors from each bootstrap replication.
est: numeric value of the estimate based on the original sample. Required for CI_type = "normal", CI_type = "basic", and CI_type = "student".
se: numeric value of the estimated standard error based on the original sample. Required for CI_type = "student".
CI_type: Character string or vector of character strings indicating types of confidence intervals to calculate. Options are "normal", "basic", "student", and "percentile" (the default).
level: numeric value between 0 and 1 for the desired coverage level, with a default of 0.95.
B_vals: vector of sub-sample sizes for which to calculate confidence intervals. Setting B_vals = length(boot_est) (the default) will return bootstrap confidence intervals calculated on the full set of bootstrap replications. For B_vals < length(boot_est), confidence intervals will be calculated after sub-sampling (without replacement) the bootstrap replications.
reps: integer value for the number of sub-sample confidence intervals to generate when B_vals < length(boot_est), with a default of reps = 1.
format: character string controlling the format of the output. If format = "wide" (the default), then different types of confidence intervals will be returned in separate columns. If format = "long", then confidence intervals of different types will appear on different rows of dataset. If format = "wide-list", then different types of confidence intervals will be returned in separate columns and the result will be wrapped in an unnamed list.
seed: Single numeric value to which the random number generator seed will be set. Default is NULL, which does not set a seed.

Value

If format = "wide", the function returns a data.frame

with reps rows per entry of B_vals, where each row contains confidence intervals for one sub-sample replication.

If format = "long", the function returns a data.frame with one row for each CI_type, each replication, and each entry of

B_vals, where each row contains a single confidence interval for one sub-sample replication.

If format = "wide-list", then the output will be structured as in

format = "wide" but will be wrapped in an unnamed list, which makes it easier to sore the output in a tibble, and will be assigned the class

"bootstrap_CIs".

Details

Confidence intervals are calculated following the methods described in Chapter 5 of Davison and Hinkley (1997). For basic non-parametric bootstraps, the methods are nearly identical to the implementation in boot.ci from the boot package.

References

Davison, A.C. and Hinkley, D.V. (1997). _Bootstrap Methods and Their Application_, Chapter 5. Cambridge University Press.

Examples

# generate t-distributed data
N <- 50
mu <- 2
nu <- 5
dat <- mu + rt(N, df = nu)

# create bootstrap replications
f <- \(x) {
 c(
   M = mean(x, trim = 0.1),
   SE = sd(x) / sqrt(length(x))
 )
}

booties <- replicate(399, {
  sample(dat, replace = TRUE, size = N) |>
  f()
})

res <- f(dat)

# calculate bootstrap CIs from full set of bootstrap replicates
bootstrap_CIs(
  boot_est = booties[1,],
  boot_se = booties[2,],
  est = res[1],
  se = res[2],
  CI_type = c("normal","basic","student","percentile"),
  format = "long"
)
#>   bootstraps       type    lower    upper
#> 1        399     normal 1.956827 2.713912
#> 2        399      basic 1.932965 2.698004
#> 3        399    student 1.916762 2.720168
#> 4        399 percentile 1.969730 2.734769

# calculate multiple bootstrap CIs using sub-sampling of replicates
bootstrap_CIs(
  boot_est = booties[1,],
  boot_se = booties[2,],
  est = res[1],
  se = res[2],
  CI_type = c("normal","basic","student","percentile"),
  B_vals = 199,
  reps = 4L,
  format = "long"
)
#>    bootstraps       type    lower    upper
#> 1         199     normal 1.962246 2.704077
#> 2         199      basic 1.932965 2.687525
#> 3         199    student 1.916762 2.720168
#> 4         199 percentile 1.980209 2.734769
#> 5         199     normal 1.980325 2.677669
#> 6         199      basic 1.947668 2.691840
#> 7         199    student 1.929162 2.704623
#> 8         199 percentile 1.975895 2.720066
#> 9         199     normal 1.962055 2.699546
#> 10        199      basic 1.932965 2.698004
#> 11        199    student 1.915225 2.704483
#> 12        199 percentile 1.969730 2.734769
#> 13        199     normal 1.971123 2.694702
#> 14        199      basic 1.962497 2.691840
#> 15        199    student 1.948314 2.704483
#> 16        199 percentile 1.975895 2.705237

# calculate multiple bootstrap CIs using sub-sampling of replicates,
# for each of several sub-sample sizes.
bootstrap_CIs(
  boot_est = booties[1,],
  boot_se = booties[2,],
  est = res[1],
  se = res[2],
  CI_type = c("normal","basic","student","percentile"),
  B_vals = c(49,99,199),
  reps = 4L,
  format = "long"
)
#>    bootstraps       type    lower    upper
#> 1          49     normal 1.983246 2.657481
#> 2          49      basic 1.935747 2.655371
#> 3          49    student 1.900402 2.658263
#> 4          49 percentile 2.012363 2.731987
#> 5          49     normal 1.925421 2.741237
#> 6          49      basic 2.013102 2.706281
#> 7          49    student 1.999313 2.720485
#> 8          49 percentile 1.961454 2.654633
#> 9          49     normal 1.962511 2.691241
#> 10         49      basic 2.046974 2.686846
#> 11         49    student 2.023731 2.749270
#> 12         49 percentile 1.980888 2.620760
#> 13         49     normal 1.856480 2.672109
#> 14         49      basic 1.869076 2.691840
#> 15         49    student 1.884228 2.720485
#> 16         49 percentile 1.975895 2.798658
#> 17         99     normal 1.947210 2.714605
#> 18         99      basic 1.935747 2.706281
#> 19         99    student 1.916762 2.703522
#> 20         99 percentile 1.961454 2.731987
#> 21         99     normal 1.942369 2.716418
#> 22         99      basic 1.947668 2.691840
#> 23         99    student 1.929162 2.720485
#> 24         99 percentile 1.975895 2.720066
#> 25         99     normal 1.933542 2.720124
#> 26         99      basic 1.907278 2.665325
#> 27         99    student 1.915225 2.688357
#> 28         99 percentile 2.002410 2.760457
#> 29         99     normal 2.007789 2.709735
#> 30         99      basic 2.016382 2.691840
#> 31         99    student 2.023731 2.720485
#> 32         99 percentile 1.975895 2.651352
#> 33        199     normal 1.945952 2.718207
#> 34        199      basic 1.902470 2.746083
#> 35        199    student 1.914183 2.757393
#> 36        199 percentile 1.921651 2.765264
#> 37        199     normal 1.972022 2.676960
#> 38        199      basic 1.932965 2.655265
#> 39        199    student 1.915225 2.694993
#> 40        199 percentile 2.012469 2.734769
#> 41        199     normal 1.944953 2.693485
#> 42        199      basic 1.907278 2.691840
#> 43        199    student 1.915225 2.720485
#> 44        199 percentile 1.975895 2.760457
#> 45        199     normal 1.959076 2.733094
#> 46        199      basic 1.950599 2.706281
#> 47        199    student 1.943938 2.749270
#> 48        199 percentile 1.961454 2.717136