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Blocked Weighted Bootstrap

Source: R/bbw.R
bbw.Rd

The blocked weighted bootstrap (BBW) is an estimation technique for use with data from two-stage cluster sampled surveys in which either prior weighting (e.g. population proportional sampling or PPS as used in Standardized Monitoring and Assessment of Relief and Transitions or SMART surveys) or posterior weighting (e.g. as used in Rapid Assessment Method or RAM and Simple Spatial Sampling Method or S3M surveys).

Details

The bootstrap technique is described in this article. The BBW used in RAM and S3M is a modification to the percentile bootstrap to include blocking and weighting to account for a complex sample design.

With RAM and S3M surveys, the sample is complex in the sense that it is an unweighted cluster sample. Data analysis procedures need to account for the sample design. A blocked weighted bootstrap (BBW) can be used:

Blocked

The block corresponds to the primary sampling unit (\(PSU = cluster\)). PSUs are resampled with replacement. Observations within the resampled PSUs are also sampled with replacement.

Weighted

RAM and S3M samples do not use population proportional sampling (PPS) to weight the sample prior to data collection (e.g. as is done with SMART surveys). This means that a posterior weighting procedure is required. bbw uses a "roulette wheel" algorithm to weight (i.e. by population) the selection probability of PSUs in bootstrap replicates.

In the case of prior weighting by PPS all clusters are given the same weight. With posterior weighting (as in RAM or S3M) the weight is the population of each PSU. This procedure is very similar to the fitness proportionate selection technique used in evolutionary computing.

A total of \(m\) PSUs are sampled with replacement for each bootstrap replicate (where \(m\) is the number of PSUs in the survey sample).

The required statistic is applied to each replicate. The reported estimate consists of the 0.025th (95% LCL), 0.5th (point estimate), and 0.975th (95% UCL) quantiles of the distribution of the statistic across all survey replicates.

Early versions of the bbw did not resample observations within PSUs following:

Cameron AC, Gelbach JB, Miller DL, Bootstrap-based improvements for inference with clustered errors, Review of Economics and Statistics, 2008:90;414–427 https://doi.org/10.1162/rest.90.3.414

and used a large number (e.g. \(3999\)) survey replicates. Current versions of the bbw resample observations within PSUs and use a smaller number of survey replicates (e.g. \(n = 400\)). This is a more computationally efficient approach

See also

Useful links:

Author

Maintainer: Ernest Guevarra ernestgmd@gmail.com (ORCID)

Authors: