C++ version: given a survey dataset and a description of the survey design (ie, which combination of vars determines primary sampling units, and which combination of vars determines strata), take a bunch of bootstrap samples for the rescaled bootstrap estimator (see, eg, Rust and Rao 1996).


rescaled.bootstrap.sample(,, parallel = FALSE,
  paropts = NULL, num.reps = 1)


the dataset to use

a formula describing the design of the survey (see below - TODO)


if TRUE, use parallelization (via plyr)


an optional list of arguments passed on to plyr to control details of parallelization


the number of bootstrap replication samples to draw


Note that we assume that the formula uniquely specifies PSUs. This will always be true if the PSUs were selected without replacement. If they were selected with replacement, then it will be necessary to make each realization of a given PSU in the sample a unique id. Bottom line: the code below assumes that all observations within each PSU (as identified by the design formula) are from the same draw of the PSU.

The rescaled bootstrap technique works by adjusting the estimation weights based on the number of times each row is included in the resamples. If a row is never selected, it is still included in the returned results, but its weight will be set to 0. It is therefore important to use estimators that make use of the estimation weights on the resampled datasets.

We always take m_i = n_i - 1, according to the advice presented in Rao and Wu (1988) and Rust and Rao (1996). is a formula of the form
weight ~ psu_vars + strata(strata_vars), where weight is the variable with the survey weights and psu is the variable denoting the primary sampling unit


a list with num.reps entries. each entry is a dataset which has at least the variables index (the row index of the original dataset that was resampled) and weight.scale (the factor by which to multiply the sampling weights in the original dataset).

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