Bootstrap weights for infinite populations ('with replacement' sampling) are created by sampling with replacement from the PSUs in each stratum. subbootweights() samples n-1 PSUs from the n available (Rao and Wu), bootweights samples n (Canty and Davison).

For multistage designs or those with large sampling fractions, mrbweights implements Preston's multistage rescaled bootstrap. The multistage rescaled bootstrap is still useful for single-stage designs with small sampling fractions, where it reduces to a half-sample replicate method.

bootweights(strata, psu, replicates = 50, fpc = NULL,
         fpctype = c("population", "fraction", "correction"),
         compress = TRUE)
subbootweights(strata, psu, replicates = 50, compress = TRUE)
mrbweights(clusters, stratas, fpcs, replicates=50, 



Identifier for sampling strata (top level only)


data frame of strata for all stages of sampling


Identifier for primary sampling units


data frame of identifiers for sampling units at each stage


Number of bootstrap replicates


Finite population correction (top level only)


Is fpc the population size, sampling fraction, or 1-sampling fraction?


survey_fpc object with population and sample size at each stage


Should the replicate weights be compressed?


Use the multicore package to generate the replicates in parallel


A set of replicate weights


With multicore=TRUE the resampling procedure does not use the current random seed, so the results cannot be exactly reproduced even by using set.seed()


These bootstraps are strictly appropriate only when the first stage of sampling is a simple or stratified random sample of PSUs with or without replacement, and not (eg) for PPS sampling. The functions will not enforce simple random sampling, so they can be used (approximately) for data that have had non-response corrections and other weight adjustments. It is preferable to apply these adjustments after creating the bootstrap replicate weights, but that may not be possible with public-use data.


Canty AJ, Davison AC. (1999) Resampling-based variance estimation for labour force surveys. The Statistician 48:379-391

Judkins, D. (1990), "Fay's Method for Variance Estimation" Journal of Official Statistics, 6, 223-239.

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

Rao JNK, Wu CFJ. Bootstrap inference for sample surveys. Proc Section on Survey Research Methodology. 1993 (866--871)

See also