SamplingStrata

This package offers an approach for the determination of the best stratification of a sampling frame, the one that ensures the minimum sample cost under the condition to satisfy precision constraints in a multivariate and multidomain case. This approach is based on the use of the genetic algorithm: each solution (i.e. a particular partition in strata of the sampling frame) is considered as an individual in a population; the fitness of all individuals is evaluated applying the Bethel-Chromy algorithm to calculate the sampling size satisfying precision constraints on the target estimates.

Functions in the package allow to:

• support in the preparation of required input data;
• execute the optimization step;
• analyse the obtained results of the optimisation step;
• select a sample from the new frame accordingly to the best allocation.

Functions for the execution of the genetic algorithm are a modified version of the functions in the ‘genalg’ package.

A complete illustration of all features and functions can be found at the link:

https://barcaroli.github.io/SamplingStrata/

Download the SamplingStrata cheatsheet from:

https://rstudio.com/resources/cheatsheets/

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This shiny app allows to run a complete optimisation workflow:

https://giulio-barcaroli.shinyapps.io/SamplingStrata/

Before using, remember to install the github version (1.6):

pak::pak(“barcaroli/SamplingStrata”)

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Installation

You can install SamplingStrata from github with:

install.packages("devtools")
devtools::install_github("barcaroli/SamplingStrata")

Three different methods for the optimization step

The optimization can be run by indicating three different methods, on the basis of the following:

A. if stratification variables are categorical (or reduced to) then the method is the “atomic”;

B. if stratification variables are continuous, then the method is the “continuous”;

C. if stratification variables are continuous, and there is spatial correlation among units in the sampling frame, then the required method is the “spatial”.

Complete example

Jupyter notebook:

Example with the “atomic” method

library(SamplingStrata)
# Load data ---------------------------------------------------------------------------------
data("swissmunicipalities")
head(swissmunicipalities[,c(2:6,9,22)])
# REG COM Nom HApoly Surfacesbois Airbat POPTOT# 1 4 261 Zurich 8781 2326 2884 363273# 2 1 6621 Geneve 1593 67 773 177964# 3 3 2701 Basel 2391 97 1023 166558# 4 2 351 Bern 5162 1726 1070 128634# 5 1 5586 Lausanne 4136 1635 856 124914# 6 4 230 Winterthur 6787 2807 972 90483# Define the sampling frame -----------------------------------------------------------------frame<-buildFrameDF(df=swissmunicipalities,
id="COM", # unique identifier of sampling unitsdomainvalue="REG", # domain variable (region)X= c("POPTOT","HApoly"), # stratification variablesY=c("Surfacesbois","Airbat")) # target variables
head(frame)
# id X1 X2 Y1 Y2 domainvalue# 1 261 363273 8781 2326 2884 4# 2 6621 177964 1593 67 773 1# 3 2701 166558 2391 97 1023 3# 4 351 128634 5162 1726 1070 2# 5 5586 124914 4136 1635 856 1# 6 230 90483 6787 2807 972 4# Define precision constraints ------------------------------------------------------------ndom<- length(unique(frame$domainvalue))
cv<- as.data.frame(list(DOM= rep("DOM1",ndom),
CV1= rep(0.10,ndom), # precision (cv=10%) for 'Surfacesbois'CV2= rep(0.10,ndom), # precision (cv=10%) for 'Airind'domainvalue= c(1:ndom))) # same precision constraints for all domainscv# DOM CV1 CV2 domainvalue# 1 DOM1 0.1 0.1 1# 2 DOM1 0.1 0.1 2# 3 DOM1 0.1 0.1 3# 4 DOM1 0.1 0.1 4# 5 DOM1 0.1 0.1 5# 6 DOM1 0.1 0.1 6# 7 DOM1 0.1 0.1 7# Build atomic strata ---------------------------------------------------------------------strata<- buildStrataDF(frame)
# Number of strata: 2895# ... of which with only one unit: 2894> head(strata)
head(strata)
# STRATO N M1 M2 S1 S2 COST CENS DOM1 X1 X2# 100*305 100*305 1 59 0 0 0 1 0 1 100 305# 1010*1661 1010*1661 1 983 0 0 0 1 0 1 1010 1661# 102*306 102*306 1 65 0 0 0 1 0 1 102 306# 1020*5351 1020*5351 1 1375 2 0 0 1 0 1 1020 5351# 10227*571 10227*571 1 73 48 0 0 1 0 1 10227 571# 10230*330 10230*330 1 15 2 0 0 1 0 1 10230 330# Find an initial solution and a suitable number of final strata in each domain -----------solutionKmean<- KmeansSolution(strata=strata, # atomic strataerrors=cv, # precision constraintsmaxclusters=10) # max number of strata to be evaluated # number of strata to be obtained in each domain in final solution: nstrat<- tapply(solutionKmean$suggestions, solutionKmean$domainvalue,
FUN=function(x) length(unique(x)))
nstrat# 1 2 3 4 5 6 7 # 9 8 10 9 10 9 10# Optimization step ------------------------------------------------------------------------solution<- optimStrata(method="atomic", # methodframesamp=frame, # sampling frameerrors=cv, # precision constraintsnStrata=nstrat, # strata to be obtained in the final stratificationsuggestions=solutionKmean, # initial solutioniter=50, # number of iterationspops=10) # number of stratifications evaluated at each iteration# Number of strata: 2895# ... of which with only one unit: 2894# *** Starting parallel optimization for 7 domains using 5 cores# |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=20s ## *** Sample size : 362# *** Number of strata : 59
head(solution$aggr_strata)
# STRATO M1 M2 S1 S2 N DOM1 COST CENS SOLUZ# 1 1 61.07407 17.37778 41.87780 13.22224 270 1 1 0 9.141966# 2 2 1114.66667 64.80392 555.75540 53.48631 51 1 1 0 6.985276# 3 3 57.05128 110.12821 50.51679 35.55146 39 1 1 0 3.550527# 4 4 477.31472 33.92386 351.59986 37.68313 197 1 1 0 19.010081# 5 5 3226.14286 184.00000 540.04720 80.64561 7 1 1 0 2.000000# 6 6 1805.21429 150.28571 256.07733 210.69830 14 1 1 0 7.553702# Sample selection --------------------------------------------------------------------------s<- selectSample(frame=solution$framenew, # frame with the indication of optimized strataoutstrata=solution$aggr_strata) # optimized strata with sampling units allocation # *** Sample has been drawn successfully ***# 362 units have been selected from 59 strata## ==> There have been 6 take-all strata # from which have been selected 9 units
head(s)
# DOMAINVALUE STRATO STRATUM ID X1 X2 Y1 Y2 LABEL WEIGHTS FPC# 1 1 1 195*201 5534 195 201 37 10 1 30 0.03333333# 2 1 1 172*193 5801 172 193 14 4 1 30 0.03333333# 3 1 1 349*398 5499 349 398 19 15 1 30 0.03333333# 4 1 1 2939*460 5582 2939 460 67 50 1 30 0.03333333# 5 1 1 186*309 5663 186 309 65 10 1 30 0.03333333# 6 1 1 290*421 5463 290 421 11 14 1 30 0.03333333