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Bootstrap estimate, standard error and confidence interval

Source: R/variance.R
bootstrap_estimate.Rd

Applies a statistic to the point weights and to every bootstrap replicate, and returns the estimate with its bootstrap standard error and a normal confidence interval. boot_total() and boot_mean() are the two shortcuts you will use most: a weighted total and a weighted mean of one column.

Usage

bootstrap_estimate(
  boot,
  statistic,
  level = 0.95,
  ci_type = c("normal", "t", "percentile"),
  df = NULL
)

boot_total(
  boot,
  variable,
  level = 0.95,
  ci_type = c("normal", "t", "percentile"),
  df = NULL
)

boot_mean(
  boot,
  variable,
  level = 0.95,
  ci_type = c("normal", "t", "percentile"),
  df = NULL
)

Arguments

boot

a weightflow_boot object.

statistic

a function function(w, data) returning a numeric scalar (or vector) given a weight vector and the data.

level

confidence level for the interval.

ci_type

interval type: "normal" (default, z-based), "t" (Student t with the design degrees of freedom, wider and less anticonservative with few PSUs), or "percentile" (empirical quantiles of the valid replicates).

df

degrees of freedom for the t interval; NULL (default) uses the design df stored on the object (total PSUs minus strata).

variable

name of the variable to estimate.

Value

A data frame with estimate, se, ci_lower, ci_upper.

Details

The bootstrap variance takes the replicate estimates \(\hat\theta^{*}_b\) around the point estimate \(\hat\theta\) (the mse = TRUE convention of survey), over the \(R\) valid replicates (a failed replicate is dropped, not counted), $$\widehat V_{\mathrm{boot}}(\hat\theta) = \frac{1}{R}\sum_{b=1}^{R}\big(\hat\theta^{*}_b - \hat\theta\big)^2.$$

See also

Other variance estimation: as_svydesign(), bootstrap_weights(), collect_replicate_weights(), jackknife_estimate(), jackknife_weights()

Examples

spec <- weighting_spec(sample_survey, base_weights = pw) |>
  step_calibrate(method = "raking",
                 margins = list(region = c(table(population$region))))
boot <- bootstrap_weights(spec, replicates = 50, strata = "region",
                          psu = "psu", seed = 1)
#>   bootstrap replicate 25/50
#>   bootstrap replicate 50/50
# a t interval with the design degrees of freedom (safer with few PSUs)
bootstrap_estimate(boot, function(w, d) sum(w * d$responded), ci_type = "t")
#>   estimate      se ci_lower ci_upper
#> 1 2663.277 90.4319 2483.771 2842.783