Compute nonparametric bootstrap estimate, standard error, confidence intervals and p-value for a vector of bootstrap replicate estimates.

```
boot_ci(data, select = NULL, method = c("dist", "quantile"), ci.lvl = 0.95)
boot_se(data, select = NULL)
boot_p(data, select = NULL)
boot_est(data, select = NULL)
```

- data
A data frame that containts the vector with bootstrapped estimates, or directly the vector (see 'Examples').

- select
Optional, unquoted names of variables (as character vector) with bootstrapped estimates. Required, if either

`data`

is a data frame (and no vector), and only selected variables from`data`

should be processed.- method
Character vector, indicating if confidence intervals should be based on bootstrap standard error, multiplied by the value of the quantile function of the t-distribution (default), or on sample quantiles of the bootstrapped values. See 'Details' in

`boot_ci()`

. May be abbreviated.- ci.lvl
Numeric, the level of the confidence intervals.

A data frame with either bootstrap estimate, standard error, the lower and upper confidence intervals or the p-value for all bootstrapped estimates.

The methods require one or more vectors of bootstrap replicate estimates as input.

`boot_est()`

: returns the bootstrapped estimate, simply by computing the mean value of all bootstrap estimates.`boot_se()`

: computes the nonparametric bootstrap standard error by calculating the standard deviation of the input vector.The mean value of the input vector and its standard error is used by

`boot_ci()`

to calculate the lower and upper confidence interval, assuming a t-distribution of bootstrap estimate replicates (for`method = "dist"`

, the default, which is`mean(x) +/- qt(.975, df = length(x) - 1) * sd(x)`

); for`method = "quantile"`

, 95\ confidence intervals (`quantile(x, probs = c(0.025, 0.975))`

). Use`ci.lvl`

to change the level for the confidence interval.P-values from

`boot_p()`

are also based on t-statistics, assuming normal distribution.

Carpenter J, Bithell J. Bootstrap confdence intervals: when, which, what? A practical guide for medical statisticians. Statist. Med. 2000; 19:1141-1164

[]`bootstrap()`

] to generate nonparametric bootstrap samples.

```
data(efc)
bs <- bootstrap(efc, 100)
# now run models for each bootstrapped sample
bs$models <- lapply(
bs$strap,
function(.x) lm(neg_c_7 ~ e42dep + c161sex, data = .x)
)
# extract coefficient "dependency" and "gender" from each model
bs$dependency <- vapply(bs$models, function(x) coef(x)[2], numeric(1))
bs$gender <- vapply(bs$models, function(x) coef(x)[3], numeric(1))
# get bootstrapped confidence intervals
boot_ci(bs$dependency)
#> term conf.low conf.high
#> 1 data 1.302479 1.75491
# compare with model fit
fit <- lm(neg_c_7 ~ e42dep + c161sex, data = efc)
confint(fit)[2, ]
#> 2.5 % 97.5 %
#> 1.292945 1.796430
# alternative function calls.
boot_ci(bs$dependency)
#> term conf.low conf.high
#> 1 data 1.302479 1.75491
boot_ci(bs, "dependency")
#> term conf.low conf.high
#> 1 dependency 1.302479 1.75491
boot_ci(bs, c("dependency", "gender"))
#> term conf.low conf.high
#> 1 dependency 1.3024793 1.754910
#> 2 gender -0.1838696 1.005308
boot_ci(bs, c("dependency", "gender"), method = "q")
#> term conf.low conf.high
#> 1 dependency 1.3263501 1.7280121
#> 2 gender -0.1274187 0.9603578
# compare coefficients
mean(bs$dependency)
#> [1] 1.528695
boot_est(bs$dependency)
#> term estimate
#> 1 data 1.528695
coef(fit)[2]
#> e42dep
#> 1.544687
```