Jackknife estimate, standard error and confidence interval

Applies a statistic to the point weights and to every delete-a-PSU replicate, and returns the estimate with its stratified jackknife (JKn) standard error and a normal confidence interval. jack_total() and jack_mean() are the shortcuts for a weighted total and a weighted mean of one column.

Usage

jackknife_estimate(
  jack,
  statistic,
  level = 0.95,
  ci_type = c("normal", "t"),
  df = NULL
)

jack_total(jack, variable, level = 0.95, ci_type = c("normal", "t"), df = NULL)

jack_mean(jack, variable, level = 0.95, ci_type = c("normal", "t"), df = NULL)

Arguments

jack

a weightflow_jack 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) or "t" (Student t with the design degrees of freedom). The percentile interval is not defined for the jackknife.

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 (for jack_total/jack_mean).

Value

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

Details

The stratified (JKn) variance sums each stratum's delete-a-PSU spread, $$\widehat V_{JK} = \sum_h \frac{n_h - 1}{n_h}\sum_{i \in h}\big(\hat\theta_{(hi)} - \hat\theta_h\big)^2,$$ with \(\hat\theta_{(hi)}\) the estimate with PSU \(i\) of stratum \(h\) deleted and \(\hat\theta_h\) their within-stratum mean; the unstratified JK1 uses a single stratum. No finite population correction is applied.

Note

jack_total() / jack_mean() center the replicate deviations on the per-stratum mean of the deleted-PSU estimates (the standard JKn). The survey design built by as_svrepdesign() instead uses mse = TRUE, which centers on the point estimate. Both are legitimate, so the standard errors from jack_total() and from svytotal() on the same object can differ slightly.

See also

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

Examples

spec <- weighting_spec(sample_one, base_weights = pw) |>
  step_calibrate(method = "raking",
                 margins = list(region = c(table(population$region))))
jk <- jackknife_weights(spec, strata = "region", psu = "psu", progress = FALSE)
jackknife_estimate(jk, function(w, d) sum(w * d$employed, na.rm = TRUE))
#>   estimate       se ci_lower ci_upper
#> 1 1031.456 85.28049 864.3092 1198.603