Multivariate optimal allocation for different domains in one and two stages stratified sample design. R2BEAT extends the Neyman (1934) – Tschuprow (1923) allocation method to the case of several variables, adopting a generalization of the Bethel’s proposal (1989). R2BEAT develops this methodology but, moreover, it allows to determine the sample allocation in the multivariate and multi-domains case of estimates for two-stage stratified samples. It also allows to perform both Primary Stage Units and Secondary Stage Units selection.
R2BEAT easily manages all the complexity due to the optimal sample allocation in two-stage sampling design and provides several outputs for evaluating the allocation. Its name stands for “R ‘to’ Bethel Extended Allocation for Two-stage”. It is an extension of another open-source software called Mauss-R (Multivariate Allocation of Units in Sampling Surveys), implemented by ISTAT researchers (https://www.istat.it/en/methods-and-tools/methods-and-it-tools/design/design-tools/mauss-r). Mauss-R determines the optimal sample allocation in multivariate and multi-domains estimation, for one-stage stratified samples.
To complete the suite of tools developed by Istat in order to cover the stratified sample design, we cite SamplingStrata (https://CRAN.R-project.org/package=SamplingStrata), that allows to jointly optimize both the stratification of the sampling frame and the allocation, still in the multivariate multidomain case (only for one-stage designs), and MultiWay.Sample.Allocation, that allows to determine the optimal sample allocation for multi-way stratified sampling designs and incomplete stratified sampling designs (https://www.istat.it/en/methods-and-tools/methods-and-it-tools/design/design-tools/multiwaysampleallocation).
For a complete illustration of the methodology see the vignette “R2BEAT methodology and use” (https://barcaroli.github.io/R2BEAT/articles/R2BEAT_methodology.html).
A complete example is illustrated in the vignette “Two-stage sampling design workflow” (https://barcaroli.github.io/R2BEAT/articles/R2BEAT_workflow.html).
Installation
You can install the released version of R2BEAT from CRAN with:
install.packages("R2BEAT")or the last version of R2BEAT from github with:
install.packages("devtools")
devtools::install_github("barcaroli/R2BEAT")
Example
library(R2BEAT)
#-------------------------------------------------------------------------------
# Read sampling frame
library(readr)
pop <- read_rds("https://github.com/barcaroli/R2BEAT_workflows/blob/master/pop.RDS?raw=true")
str(pop)
# 'data.frame': 2258507 obs. of 13 variables:
# $ region : Factor w/ 3 levels "north","center",..: 1 1 1 1 1 1 1 1 1 1 ...
# $ province : Factor w/ 6 levels "north_1","north_2",..: 1 1 1 1 1 1 1 1 1 1 ...
# $ municipality : num 1 1 1 1 1 1 1 1 1 1 ...
# $ id_hh : Factor w/ 963018 levels "H1","H10","H100",..: 1 1 1 2 3 3 3 3 1114 1114 ...
# $ id_ind : int 1 2 3 4 5 6 7 8 9 10 ...
# $ stratum : Factor w/ 24 levels "1000","2000",..: 12 12 12 12 12 12 12 12 12 12 ...
# $ stratum_label: chr "north_1_6" "north_1_6" "north_1_6" "north_1_6" ...
# $ sex : int 1 2 1 2 1 1 2 2 1 1 ...
# $ cl_age : Factor w/ 8 levels "(0,14]","(14,24]",..: 3 7 8 5 4 6 6 4 4 1 ...
# $ active : num 1 1 0 1 1 1 1 1 1 0 ...
# $ income_hh : num 30488 30488 30488 21756 29871 ...
# $ unemployed : num 0 0 0 0 0 0 0 0 0 0 ...
# $ inactive : num 0 0 1 0 0 0 0 0 0 1 ...
#-------------------------------------------------------------------------------
# Precision constraints
cv <- as.data.frame(list(DOM=c("DOM1","DOM2"),
CV1=c(0.02,0.03),
CV2=c(0.03,0.06),
CV3=c(0.03,0.06),
CV4=c(0.05,0.08)))
cv
# DOM CV1 CV2 CV3 CV4
# 1 DOM1 0.02 0.03 0.03 0.05
# 2 DOM2 0.03 0.06 0.06 0.08
#-------------------------------------------------------------------------------
# Preparation
samp_frame <- pop
samp_frame$one <- 1
id_PSU <- "municipality"
id_SSU <- "id_ind"
strata_var <- "stratum"
target_vars <- c("income_hh","active","inactive","unemployed")
deff_var <- "stratum"
domain_var <- "region"
delta = 1 # households = survey units
minimum <- 50 # minimum number of SSUs to be interviewed in each selected PSU
deff_sugg <- 1.5 # suggestion for the deff value
inp <- prepareInputToAllocation1(samp_frame,
id_PSU,
id_SSU,
strata_var,
target_vars,
deff_var,
domain_var,
minimum,
delta,
deff_sugg)
#-------------------------------------------------------------------------------
# Optimal allocation
alloc <- beat.2st(stratif = inp$strata,
errors = cv,
des_file = inp$des_file,
psu_file = inp$psu_file,
rho = inp$rho,
deft_start = NULL,
effst = inp$effst,
minPSUstrat = 2,
minnumstrat = 50)
# iterations PSU_SR PSU NSR PSU Total SSU
# 1 0 0 0 0 7887
# 2 1 31 104 135 8328
# 3 2 39 104 143 8317
# 4 3 38 104 142 8320
#-------------------------------------------------------------------------------
# First stage selection
sample_1st <- select_PSU(alloc, type="ALLOC", pps=TRUE, plot=TRUE)
sample_1st$PSU_stats
# STRATUM PSU PSU_SR PSU_NSR SSU SSU_SR SSU_NSR
# 1 1000 2 2 0 286 286 0
# 2 2000 9 3 6 452 152 300
# 3 3000 4 0 4 200 0 200
# 4 4000 2 0 2 100 0 100
# 5 5000 2 2 0 219 219 0
# 6 6000 2 0 2 100 0 100
# 7 7000 2 0 2 100 0 100
# 8 8000 2 0 2 100 0 100
# 9 9000 1 1 0 557 557 0
# 10 10000 6 6 0 587 587 0
# 11 11000 26 2 24 1300 100 1200
# 12 12000 8 0 8 400 0 400
# 13 13000 1 1 0 703 703 0
# 14 14000 4 4 0 577 577 0
# 15 15000 27 9 18 1361 461 900
# 16 16000 18 0 18 900 0 900
# 17 17000 1 1 0 154 154 0
# 18 18000 4 2 2 200 100 100
# 19 19000 7 1 6 350 50 300
# 20 20000 4 0 4 200 0 200
# 21 21000 1 1 0 125 125 0
# 22 22000 3 3 0 150 150 0
# 23 23000 4 0 4 200 0 200
# 24 24000 2 0 2 100 0 100
# 25 Total 142 38 104 9421 4221 5200
#-------------------------------------------------------------------------------
# Second stage selection
sample_2st <- select_SSU(df=pop,
PSU_code="municipality",
SSU_code="id_ind",
PSU_sampled=sample_1st$sample_PSU)
head(sample_2st)
# municipality id_ind region province id_hh stratum stratum_label sex cl_age active income_hh
# 1 10 1570 north north_1 H49617 12000 north_1_6 2 (64,74] 1 25393.18
# 2 10 1632 north north_1 H49638 12000 north_1_6 1 (64,74] 1 24261.16
# 3 10 1638 north north_1 H49639 12000 north_1_6 1 (24,34] 1 60761.11
# 4 10 1690 north north_1 H49656 12000 north_1_6 2 (34,44] 1 40065.25
# 5 10 1709 north north_1 H49665 12000 north_1_6 1 (44,54] 1 13320.58
# 6 10 1767 north north_1 H49682 12000 north_1_6 1 (34,44] 1 27106.55
# unemployed inactive Prob_1st Prob_2st Prob_tot weight SR nSR stratum_2
# 1 0 0 0.2363018 0.02665245 0.006298022 158.78 0 1 12000-1
# 2 0 0 0.2363018 0.02665245 0.006298022 158.78 0 1 12000-1
# 3 0 0 0.2363018 0.02665245 0.006298022 158.78 0 1 12000-1
# 4 0 0 0.2363018 0.02665245 0.006298022 158.78 0 1 12000-1
# 5 0 0 0.2363018 0.02665245 0.006298022 158.78 0 1 12000-1
# 6 0 0 0.2363018 0.02665245 0.006298022 158.78 0 1 12000-1