Stratified Sampling

Integrating a stratified structure in the population in a sampling design can considerably reduce the variance of the Horvitz-Thompson estimator. We propose in this package different methods to handle the selection of a balanced sample in stratified population. For more details see Raphaël Jauslin, Esther Eustache and Yves Tillé (2021) https://arxiv.org/abs/2101.05568.

The package propose also a method to do statistical matching using optimal transport and balanced sampling. For more details see Raphaël Jauslin and Yves Tillé (2021) https://arxiv.org/abs/2105.08379.

Installation

CRAN version

install.packages("StratifiedSampling")

Latest version

You can install the latest version of the package StratifiedSampling with the following command:

# install.packages("devtools")
devtools::install_github("Rjauslin/StratifiedSampling")

Optimal transport matching

A complete example on how to use the package to make an optimal statistical transport match can be found in the following vignette:

vignette("ot_matching", package = "StratifiedSampling")

Simple example on stratified population

This basic example shows you how to set up a stratified sampling design. The example is done on the swissmunicipalities dataset from the package sampling.

library(sampling)
library(StratifiedSampling)
#> Le chargement a nécessité le package : Matrix

data(swissmunicipalities)
swiss <- swissmunicipalities
X <- cbind(swiss$HApoly,
        swiss$Surfacesbois,
        swiss$P00BMTOT,
        swiss$P00BWTOT,
        swiss$POPTOT,
        swiss$Pop020,
        swiss$Pop2040,
        swiss$Pop4065,
        swiss$Pop65P,
        swiss$H00PTOT )

X <- X[order(swiss$REG),]
strata <- swiss$REG[order(swiss$REG)]

Strata are NUTS region of the Switzerland. Inclusion probabilities pik is set up equal within strata and such that the sum of the inclusion probabilities within strata is equal to 80.

pik <- sampling::inclusionprobastrata(strata,rep(80,7))

It remains to use the function stratifiedcube().

s <- stratifiedcube(X,strata,pik)

We can check that we have correctly selected the sample. It is balanced and have the right number of units selected in each stratum.

head(s)
#> [1] 0 0 1 0 0 0

sum(s)
#> [1] 560
t(X/pik)%*%s
#>          [,1]
#>  [1,] 3892352
#>  [2,] 1266973
#>  [3,] 4066595
#>  [4,] 4298949
#>  [5,] 8365545
#>  [6,] 1829315
#>  [7,] 2489098
#>  [8,] 2704028
#>  [9,] 1343104
#> [10,] 3680468
t(X/pik)%*%pik
#>          [,1]
#>  [1,] 3998831
#>  [2,] 1270996
#>  [3,] 3567567
#>  [4,] 3720443
#>  [5,] 7288010
#>  [6,] 1665613
#>  [7,] 2141059
#>  [8,] 2362332
#>  [9,] 1119006
#> [10,] 3115399

Xcat <- disj(strata)

t(Xcat)%*%s
#>      [,1]
#> [1,]   80
#> [2,]   80
#> [3,]   80
#> [4,]   80
#> [5,]   80
#> [6,]   80
#> [7,]   80
t(Xcat)%*%pik
#>      [,1]
#> [1,]   80
#> [2,]   80
#> [3,]   80
#> [4,]   80
#> [5,]   80
#> [6,]   80
#> [7,]   80