Bootstrap confidence intervals

Calculate bootstrap confidence intervals using various methods.

Usage

int_pctl(.data, ...)

# S3 method for bootstraps
int_pctl(.data, statistics, alpha = 0.05, ...)

int_t(.data, ...)

# S3 method for bootstraps
int_t(.data, statistics, alpha = 0.05, ...)

int_bca(.data, ...)

# S3 method for bootstraps
int_bca(.data, statistics, alpha = 0.05, .fn, ...)

Arguments

.data

A data frame containing the bootstrap resamples created using bootstraps(). For t- and BCa-intervals, the apparent argument should be set to TRUE. Even if the apparent argument is set to TRUE for the percentile method, the apparent data is never used in calculating the percentile confidence interval.

...

Arguments to pass to .fn (int_bca() only).

statistics

An unquoted column name or dplyr selector that identifies a single column in the data set containing the individual bootstrap estimates. This must be a list column of tidy tibbles (with columns term and estimate). For t-intervals, a standard tidy column (usually called std.err) is required. See the examples below.

alpha

Level of significance.

.fn

A function to calculate statistic of interest. The function should take an rsplit as the first argument and the ... are required.

Value

Each function returns a tibble with columns .lower, .estimate, .upper, .alpha, .method, and term. .method is the type of interval (eg. "percentile", "student-t", or "BCa"). term is the name of the estimate. Note the .estimate returned from int_pctl()

is the mean of the estimates from the bootstrap resamples and not the estimate from the apparent model.

Details

Percentile intervals are the standard method of obtaining confidence intervals but require thousands of resamples to be accurate. T-intervals may need fewer resamples but require a corresponding variance estimate. Bias-corrected and accelerated intervals require the original function that was used to create the statistics of interest and are computationally taxing.

References

https://rsample.tidymodels.org/articles/Applications/Intervals.html

Davison, A., & Hinkley, D. (1997). Bootstrap Methods and their Application. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511802843

See also

reg_intervals()

Examples

# \donttest{
library(broom)
library(dplyr)
library(purrr)
library(tibble)

lm_est <- function(split, ...) {
  lm(mpg ~ disp + hp, data = analysis(split)) %>%
    tidy()
}

set.seed(52156)
car_rs <-
  bootstraps(mtcars, 500, apparent = TRUE) %>%
  mutate(results = map(splits, lm_est))

int_pctl(car_rs, results)
#> Warning: Recommend at least 1000 non-missing bootstrap resamples for terms: `(Intercept)`, `disp`, `hp`.
#> # A tibble: 3 × 6
#>   term         .lower .estimate   .upper .alpha .method   
#>   <chr>         <dbl>     <dbl>    <dbl>  <dbl> <chr>     
#> 1 (Intercept) 27.5      30.7    33.6       0.05 percentile
#> 2 disp        -0.0440   -0.0300 -0.0162    0.05 percentile
#> 3 hp          -0.0572   -0.0260 -0.00840   0.05 percentile
int_t(car_rs, results)
#> # A tibble: 3 × 6
#>   term         .lower .estimate   .upper .alpha .method  
#>   <chr>         <dbl>     <dbl>    <dbl>  <dbl> <chr>    
#> 1 (Intercept) 28.1      30.7    34.6       0.05 student-t
#> 2 disp        -0.0446   -0.0300 -0.0170    0.05 student-t
#> 3 hp          -0.0449   -0.0260 -0.00337   0.05 student-t
int_bca(car_rs, results, .fn = lm_est)
#> Warning: Recommend at least 1000 non-missing bootstrap resamples for terms: `(Intercept)`, `disp`, `hp`.
#> # A tibble: 3 × 6
#>   term         .lower .estimate   .upper .alpha .method
#>   <chr>         <dbl>     <dbl>    <dbl>  <dbl> <chr>  
#> 1 (Intercept) 27.7      30.7    33.7       0.05 BCa    
#> 2 disp        -0.0446   -0.0300 -0.0172    0.05 BCa    
#> 3 hp          -0.0576   -0.0260 -0.00843   0.05 BCa    

# putting results into a tidy format
rank_corr <- function(split) {
  dat <- analysis(split)
  tibble(
    term = "corr",
    estimate = cor(dat$sqft, dat$price, method = "spearman"),
    # don't know the analytical std.err so no t-intervals
    std.err = NA_real_
  )
}

set.seed(69325)
data(Sacramento, package = "modeldata")
bootstraps(Sacramento, 1000, apparent = TRUE) %>%
  mutate(correlations = map(splits, rank_corr)) %>%
  int_pctl(correlations)
#> # A tibble: 1 × 6
#>   term  .lower .estimate .upper .alpha .method   
#>   <chr>  <dbl>     <dbl>  <dbl>  <dbl> <chr>     
#> 1 corr   0.737     0.768  0.796   0.05 percentile
# }