Sequential Poisson sampling is a variation of Poisson sampling for drawing probability-proportional-to-size samples with a given number of units, and is commonly used for price-index surveys. This package gives functions to draw stratified sequential Poisson samples according to the method by Ohlsson (1998), and generate appropriate bootstrap replicate weights according to the generalized bootstrap method by Beaumont and Patak (2012).
install.packages("sps")The development version can be found on GitHub.
devtools::install_github("marberts/sps")Given a vector of sizes for units in a population (e.g., revenue for
sampling businesses) and a desired sample size, a stratified sequential
Poisson sample can be drawn with the sps() function.
library(sps)
# Generate some data on sizes for 12 businesses in a single
# stratum as a simple example
revenue <- c(1:10, 100, 150)
# Draw a sample of 6 businesses
(samp <- sps(revenue, 6))
#> [1] 4 7 8 10 11 12
# Design weights and sampling strata are stored with the sample
weights(samp)
#> [1] 3.437500 1.964286 1.718750 1.375000 1.000000 1.000000
levels(samp)
#> [1] "TS" "TS" "TS" "TS" "TA" "TA"Allocations are often proportional to size when drawing such samples,
and the prop_allocation() function provides a variety of
methods for generating proportional-to-size allocations.
# Add some strata
stratum <- rep(c("a", "b"), c(9, 3))
# Make an allocation
(allocation <- prop_allocation(revenue, 6, stratum))
#> a b
#> 3 3
# Draw a stratified sample
(samp <- sps(revenue, allocation, stratum))
#> [1] 4 7 9 10 11 12
weights(samp)
#> [1] 3.750000 2.142857 1.666667 1.000000 1.000000 1.000000
levels(samp)
#> [1] "TS" "TS" "TS" "TA" "TA" "TA"The design weights for a sample can then be used to generate
bootstrap replicate weights with the sps_repwights()
function.
sps_repweights(weights(samp), 5, tau = 2)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 3.625000 3.625000 3.625000 5.500000 2.2500000
#> [2,] 2.214286 2.214286 2.214286 2.214286 1.7142857
#> [3,] 2.000000 1.500000 1.166667 2.333333 0.6666667
#> [4,] 1.000000 1.000000 1.000000 1.000000 1.0000000
#> [5,] 1.000000 1.000000 1.000000 1.000000 1.0000000
#> [6,] 1.000000 1.000000 1.000000 1.000000 1.0000000Beaumont, J.-F. and Patak, Z. (2012). On the Generalized Bootstrap for Sample Surveys with Special Attention to Poisson Sampling. International Statistical Review, 80(1): 127-148.
Ohlsson, E. (1998). Sequential Poisson Sampling. Journal of Official Statistics, 14(2): 149-162.