rescaled.bootstrap.sample

Given a survey dataset and a description of the survey design (ie, which combination of variables determines primary sampling units, and which combination of variables determines strata), take a bunch of bootstrap samples for the rescaled bootstrap estimator (see Details).

Usage

rescaled.bootstrap.sample(
  survey.data,
  survey.design,
  parallel = FALSE,
  paropts = NULL,
  num.reps = 1,
  include_cc = FALSE
)

Arguments

survey.data

The dataset to use

survey.design

A formula describing the design of the survey (see Details)

parallel

If TRUE, use parallelization (via plyr)

paropts

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

num.reps

The number of bootstrap replication samples to draw

include_cc

If TRUE, include cluster counts in the output. These cluster counts are needed for jackknife after bootstrap calculations

Value

The return value will depend on whether or not you ask for the cluster counts (using `include_cc`).
If `include_cc` is `FALSE` (the default), return
  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).

 If `include_cc` is `TRUE`, then return a list with two entries:

* `weight_scaling_factor` - 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).
* `cluster_counts` - A list with `num.reps` entries.
  Each entry is a dataset which has the variable '.cluster_id',
  the values of columns that specify the PSU (from the `survey.design` formula),
  and `cluster_count` (the number of times the given PSU was resampled))

Details

survey.design is a formula of the form

weight ~ psu_vars + strata(strata_vars)

where:

• weight is the variable with the survey weights

• psu_vars has the form psu_v1 + psu_v2 + ..., where primary sampling units (PSUs) are determined by psu_v1, etc

• strata_vars has the form strata_v1 + strata_v2 + ..., which determine strata

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. 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).

(This is a C++ version; a previous version, written in pure R, is called rescaled.bootstrap.sample.pureR() )

References:

• Rust, Keith F., and J. N. K. Rao. "Variance estimation for complex surveys using replication techniques." Statistical methods in medical research 5.3 (1996): 283-310.

• Rao, Jon NK, and C. F. J. Wu. "Resampling inference with complex survey data." Journal of the American Statistical Association 83.401 (1988): 231-241.

Examples

survey <- MU284.complex.surveys[[1]]
boot_surveys <- rescaled.bootstrap.sample(survey.data = survey,
                                          survey.design = ~ CL,
                                          num.reps = 2)