Calculate one or multiple bootstrap confidence intervals
Source:R/bootstrap-projection.R
bootstrap_CIs.RdCalculate one or multiple bootstrap confidence intervals, given a sample of bootstrap replications.
Usage
bootstrap_CIs(
boot_est,
boot_se = NULL,
est = NULL,
se = NULL,
influence = 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",CI_type = "student", andCI_type = "bias-corrected".- se
numeric value of the estimated standard error based on the original sample. Required for
CI_type = "student".- influence
vector of empirical influence values for the estimator. Required for
CI_type = "BCa".- CI_type
Character string or vector of character strings indicating types of confidence intervals to calculate. Options are
"normal","basic","student","percentile"(the default),"bias-corrected", or"BCa".- 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. ForB_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 ofreps = 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. Ifformat = "long", then confidence intervals of different types will appear on different rows of dataset. Ifformat = "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","bias-corrected"),
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
#> 5 399 bias-corrected 1.980209 2.737876
# Calculate bias-corrected-and-accelerated CIs
inf_vals <- res[1] - sapply(seq_along(dat), \(i) f(dat[-i])[1])
bootstrap_CIs(
boot_est = booties[1,],
est = res[1],
influence = inf_vals,
CI_type = c("percentile","bias-corrected","BCa"),
format = "long"
)
#> bootstraps type lower upper
#> 1 399 percentile 1.969730 2.734769
#> 2 399 bias-corrected 1.980209 2.737876
#> 3 399 BCa 1.980209 2.737876
# 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","bias-corrected"),
B_vals = 199,
reps = 4L,
format = "long"
)
#> bootstraps type lower upper
#> 1 199 normal 1.980454 2.694244
#> 2 199 basic 1.950599 2.698004
#> 3 199 student 1.943938 2.704483
#> 4 199 percentile 1.969730 2.717136
#> 5 199 bias-corrected 1.980209 2.717136
#> 6 199 normal 1.971123 2.694702
#> 7 199 basic 1.962497 2.691840
#> 8 199 student 1.948314 2.704483
#> 9 199 percentile 1.975895 2.705237
#> 10 199 bias-corrected 2.002991 2.760457
#> 11 199 normal 1.947918 2.691788
#> 12 199 basic 1.920147 2.691840
#> 13 199 student 1.915225 2.720168
#> 14 199 percentile 1.975895 2.747588
#> 15 199 bias-corrected 1.961454 2.705237
#> 16 199 normal 1.940259 2.719847
#> 17 199 basic 1.920147 2.691840
#> 18 199 student 1.916762 2.704623
#> 19 199 percentile 1.975895 2.747588
#> 20 199 bias-corrected 1.961454 2.661461
# 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 1.954279 2.756996
#> 2 49 basic 2.004221 2.686558
#> 3 49 student 1.987738 2.701393
#> 4 49 percentile 1.981176 2.663513
#> 5 49 normal 1.940103 2.700159
#> 6 49 basic 1.901757 2.641634
#> 7 49 student 1.901939 2.672398
#> 8 49 percentile 2.026100 2.765978
#> 9 49 normal 2.009940 2.709993
#> 10 49 basic 2.016382 2.664743
#> 11 49 student 2.023731 2.704483
#> 12 49 percentile 2.002991 2.651352
#> 13 49 normal 2.005915 2.723204
#> 14 49 basic 2.109050 2.691840
#> 15 49 student 2.101210 2.720485
#> 16 49 percentile 1.975895 2.558685
#> 17 99 normal 1.943855 2.668960
#> 18 99 basic 1.907278 2.654617
#> 19 99 student 1.901939 2.650926
#> 20 99 percentile 2.013117 2.760457
#> 21 99 normal 1.959127 2.709051
#> 22 99 basic 1.907278 2.686846
#> 23 99 student 1.926578 2.720168
#> 24 99 percentile 1.980888 2.760457
#> 25 99 normal 1.995844 2.670863
#> 26 99 basic 1.993127 2.655265
#> 27 99 student 1.982072 2.704483
#> 28 99 percentile 2.012469 2.674607
#> 29 99 normal 1.965503 2.729939
#> 30 99 basic 1.920147 2.746083
#> 31 99 student 1.900402 2.756335
#> 32 99 percentile 1.921651 2.747588
#> 33 199 normal 1.954786 2.688914
#> 34 199 basic 1.932965 2.686846
#> 35 199 student 1.926578 2.720168
#> 36 199 percentile 1.980888 2.734769
#> 37 199 normal 1.956729 2.736172
#> 38 199 basic 1.947668 2.746083
#> 39 199 student 1.929162 2.757393
#> 40 199 percentile 1.921651 2.720066
#> 41 199 normal 1.953180 2.728824
#> 42 199 basic 1.920147 2.720873
#> 43 199 student 1.916762 2.749270
#> 44 199 percentile 1.946861 2.747588
#> 45 199 normal 1.963244 2.708885
#> 46 199 basic 1.920147 2.691840
#> 47 199 student 1.901939 2.694993
#> 48 199 percentile 1.975895 2.747588