Convert a survey design object to a bootstrap replicate design

Converts a survey design object to a replicate design object with replicate weights formed using a bootstrap method. Supports stratified, cluster samples with one or more stages of sampling. At each stage of sampling, either simple random sampling (with or without replacement) or unequal probability sampling (with or without replacement) may be used.

Usage

as_bootstrap_design(
  design,
  type = "Rao-Wu-Yue-Beaumont",
  replicates = 500,
  compress = TRUE,
  mse = getOption("survey.replicates.mse"),
  samp_method_by_stage = NULL
)

Arguments

design

A survey design object created using the 'survey' (or 'srvyr') package, with class 'survey.design' or 'svyimputationList'.

type

The type of bootstrap to use, which should be chosen based on its applicability to the sampling method used for the survey. The available types are the following:

"Rao-Wu-Yue-Beaumont" (the default):
The bootstrap method of Beaumont and Émond (2022), which is a generalization of the Rao-Wu-Yue bootstrap, and is applicable to a wide variety of designs, including single-stage and multistage stratified designs. The design may have different sampling methods used at different stages. Each stage of sampling may potentially be PPS (i.e., use unequal probabilities), with or without replacement, and may potentially use Poisson sampling.

For a stratum with a fixed sample size of \(n\) sampling units, resampling in each replicate resamples \((n-1)\) sampling units with replacement.
"Rao-Wu":
The basic Rao-Wu \((n-1)\) bootstrap method, which is only applicable to single-stage designs or multistage designs where the first-stage sampling fractions are small (and can thus be ignored). Accommodates stratified designs. All sampling within a stratum must be simple random sampling with or without replacement, although the first-stage sampling is effectively treated as sampling without replacement.
"Preston":
Preston's multistage rescaled bootstrap, which is applicable to single-stage designs or multistage designs with arbitrary sampling fractions. Accommodates stratified designs. All sampling within a stratum must be simple random sampling with or without replacement.
"Canty-Davison":
The Canty-Davison bootstrap, which is only applicable to single-stage designs, with arbitrary sampling fractions. Accommodates stratified designs. All sampling with a stratum must be simple random sampling with or without replacement.

replicates

Number of bootstrap replicates (should be as large as possible, given computer memory/storage limitations). A commonly-recommended default is 500.

compress

Use a compressed representation of the replicate weights matrix. This reduces the computer memory required to represent the replicate weights and has no impact on estimates.

mse

If TRUE, compute variances from sums of squares around the point estimate from the full-sample weights, If FALSE, compute variances from sums of squares around the mean estimate from the replicate weights.

samp_method_by_stage

(Optional). By default, this function will automatically determine the sampling method used at each stage. However, this argument can be used to ensure the correct sampling method is identified for each stage.
Accepts a vector with length equal to the number of stages of sampling. Each element should be one of the following:

"SRSWOR" - Simple random sampling, without replacement
"SRSWR" - Simple random sampling, with replacement
"PPSWOR" - Unequal probabilities of selection, without replacement
"PPSWR" - Unequal probabilities of selection, with replacement
"Poisson" - Poisson sampling: each sampling unit is selected into the sample at most once, with potentially different probabilities of inclusion for each sampling unit.

Value

A replicate design object, with class svyrep.design, which can be used with the usual functions, such as svymean() or svyglm().

Use weights(..., type = 'analysis') to extract the matrix of replicate weights.

Use as_data_frame_with_weights() to convert the design object to a data frame with columns for the full-sample and replicate weights.

References

Beaumont, J.-F.; Émond, N. (2022). "A Bootstrap Variance Estimation Method for Multistage Sampling and Two-Phase Sampling When Poisson Sampling Is Used at the Second Phase." Stats, 5: 339–357. https://doi.org/10.3390/stats5020019

Canty, A.J.; Davison, A.C. (1999). "Resampling-based variance estimation for labour force surveys." The Statistician, 48: 379-391.

Preston, J. (2009). "Rescaled bootstrap for stratified multistage sampling." Survey Methodology, 35(2): 227-234.

Rao, J.N.K.; Wu, C.F.J.; Yue, K. (1992). "Some recent work on resampling methods for complex surveys." Survey Methodology, 18: 209–217.

Examples

library(survey)
# Example 1: A multistage sample with two stages of SRSWOR

  ## Load an example dataset from a multistage sample, with two stages of SRSWOR
  data("mu284", package = 'survey')
  multistage_srswor_design <- svydesign(data = mu284,
                                        ids = ~ id1 + id2,
                                        fpc = ~ n1 + n2)

  ## Convert the survey design object to a bootstrap design
  set.seed(2022)
  bootstrap_rep_design <- as_bootstrap_design(multistage_srswor_design,
                                              replicates = 500)

  ## Compare std. error estimates from bootstrap versus linearization
  data.frame(
    'Statistic' = c('total', 'mean', 'median'),
    'SE (bootstrap)' = c(SE(svytotal(x = ~ y1, design = bootstrap_rep_design)),
                         SE(svymean(x = ~ y1, design = bootstrap_rep_design)),
                         SE(svyquantile(x = ~ y1, quantile = 0.5,
                                        design = bootstrap_rep_design))),
    'SE (linearization)' = c(SE(svytotal(x = ~ y1, design = multistage_srswor_design)),
                             SE(svymean(x = ~ y1, design = multistage_srswor_design)),
                             SE(svyquantile(x = ~ y1, quantile = 0.5,
                                            design = multistage_srswor_design))),
    check.names = FALSE
  )
#>   Statistic SE (bootstrap) SE (linearization)
#> 1     total    2311.130145        2274.254701
#> 2      mean       2.449955           2.273653
#> 3    median       2.331234           2.521210

# Example 2: A multistage-sample,
# first stage selected with unequal probabilities without replacement
# second stage selected with simple random sampling without replacement

  data("library_multistage_sample", package = "svrep")

  multistage_pps <- svydesign(data = library_multistage_sample,
                              ids = ~ PSU_ID + SSU_ID,
                              fpc = ~ PSU_SAMPLING_PROB + SSU_SAMPLING_PROB,
                              pps = "brewer")

  bootstrap_rep_design <- as_bootstrap_design(
    multistage_pps, replicates = 500,
    samp_method_by_stage = c("PPSWOR", "SRSWOR")
  )

  ## Compare std. error estimates from bootstrap versus linearization
  data.frame(
      'Statistic' = c('total', 'mean'),
      'SE (bootstrap)' = c(
          SE(svytotal(x = ~ TOTCIR, na.rm = TRUE,
                      design = bootstrap_rep_design)),
          SE(svymean(x = ~ TOTCIR, na.rm = TRUE,
                     design = bootstrap_rep_design))),
      'SE (linearization)' = c(
          SE(svytotal(x = ~ TOTCIR, na.rm = TRUE,
                      design = multistage_pps)),
          SE(svymean(x = ~ TOTCIR, na.rm = TRUE,
                     design = multistage_pps))),
      check.names = FALSE
  )
#>   Statistic SE (bootstrap) SE (linearization)
#> 1     total   266151536.55       255100437.38
#> 2      mean       45762.71           42544.16