Get the scale coefficients used for variance estimation in a replicate design object.
Arguments
- rep_design
A replicate design object
- type
Either
'overall','specific', or'combined'. See the details section below. The result for'overall'is the single overall scale coefficient. The result for'specific'is the vector of replicate-specific coefficients. The result for'combined'is the product of the overall and replicate-specific coefficients.
Value
If type = 'overall', the result is a single number.
Otherwise, the result is a vector with length matching
the number of replicates.
Details
For a statistic \(\hat{\theta}\), replication methods estimate the sampling variance using \(R\) replicate estimates, with the estimate for the \(r\)-th replicate denoted \(\hat{\theta}_r\).
The formula for the variance estimate is the following: $$ v(\hat{\theta}) = C \sum_{r=1}^{R} c_r (\hat{\theta_r} - \hat{\theta})^2 $$
The terms \(C\) and \(c_r, r=1,\dots,R\) are scale coefficients. \(C\) is the overall coefficient, and \(c_r, r=1,\dots,R\) are replicate-specific coefficients.
Specifying get_rep_scale_coefs(type='overall') returns
the overall coefficient \(C\). Specifying type='specific'
returns the replicate-specific coefficients \(c_r, r=1,\dots,R\).
Specifying type='combined' returns a vector with
\(R\) elements,
where the \(r\)-th element is \(C \times c_r\).
Examples
data('api', package = 'survey')
api_design <- svydesign(
data = apistrat,
id = ~ 1,
strata = ~ stype,
weights = ~ pw,
nest = TRUE
)
jk_design <- api_design |>
as_random_group_jackknife_design(
replicates = 12
)
jk_design |>
get_rep_scale_coefs('overall')
#> [1] 1
jk_design |>
get_rep_scale_coefs('specific')
#> [1] 0.915 0.915 0.915 0.915 0.915 0.915 0.915 0.915 0.920 0.920 0.920 0.920
jk_design |>
get_rep_scale_coefs('combined')
#> [1] 0.915 0.915 0.915 0.915 0.915 0.915 0.915 0.915 0.920 0.920 0.920 0.920