svrep (version 0.7.0)

subsample_replicates: Retain only a random subset of the replicates in a design

Description

Randomly subsamples the replicates of a survey design object, to keep only a subset. The scale factor used in estimation is increased to account for the subsampling.

Usage

subsample_replicates(design, n_reps)

Value

An updated survey design object, where only a random selection of the replicates has been retained. The overall 'scale' factor for the design (accessed with design$scale) is increased to account for the sampling of replicates.

Arguments

design

A survey design object, created with either the survey or srvyr packages.

n_reps

The number of replicates to keep after subsampling

Statistical Details

Suppose the initial replicate design has \(L\) replicates, with respective constants \(c_k\) for \(k=1,\dots,L\) used to estimate variance with the formula $$v_{R} = \sum_{k=1}^L c_k\left(\hat{T}_y^{(k)}-\hat{T}_y\right)^2$$

With subsampling of replicates, \(L_0\) of the original \(L\) replicates are randomly selected, and then variances are estimated using the formula: $$v_{R} = \frac{L}{L_0} \sum_{k=1}^{L_0} c_k\left(\hat{T}_y^{(k)}-\hat{T}_y\right)^2$$

This subsampling is suggested for certain replicate designs in Fay (1989). Kim and Wu (2013) provide a detailed theoretical justification and also propose alternative methods of subsampling replicates.

References

Fay, Robert. 1989. "Theory And Application Of Replicate Weighting For Variance Calculations." In, 495–500. Alexandria, VA: American Statistical Association. http://www.asasrms.org/Proceedings/papers/1989_033.pdf

Kim, J.K. and Wu, C. 2013. "Sparse and Efficient Replication Variance Estimation for Complex Surveys." Survey Methodology, Statistics Canada, 39(1), 91-120.

Examples

library(survey)
set.seed(2023)

# Create an example survey design object

  sample_data <- data.frame(
    STRATUM = c(1,1,1,1,2,2,2,2),
    PSU     = c(1,2,3,4,5,6,7,8)
  )

  survey_design <- svydesign(
    data = sample_data,
    strata = ~ STRATUM,
    ids = ~ PSU,
    weights = ~ 1
  )

  rep_design <- survey_design |>
    as_fays_gen_rep_design(variance_estimator = "Ultimate Cluster")

# Inspect replicates before subsampling

  rep_design |> getElement("repweights")

# Inspect replicates after subsampling

  rep_design |>
    subsample_replicates(n_reps = 4) |>
    getElement("repweights")