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 allows to:
- support in the preparation of required input data;
- execute the optimisation 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/
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”.
Example with the “continuous” 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 units domainvalue= "REG", # domain variable (region) X = c("POPTOT","HApoly"), # stratification variables Y =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$domainvalue)) cv <- as.data.frame(list(DOM = rep("DOM1",ndom), CV1 = rep(0.10,ndom), # precision (cv=10%) for 'Surfacesbois' CV2 = rep(0.10,ndom), # precision (cv=10%) for 'Airind' domainvalue= c(1:ndom))) # same precision constraints for all domains cv # DOM CV1 CV2 domainvalue # 1 DOM1 0.1 0.1 1 # 2 DOM1 0.1 0.1 2 # 3 DOM1 0.1 0.1 3 # 4 DOM1 0.1 0.1 4 # 5 DOM1 0.1 0.1 5 # 6 DOM1 0.1 0.1 6 # 7 DOM1 0.1 0.1 7 # Find an initial solution and a suitable number of final strata in each domain ----------- solutionKmean <- KmeansSolution2(frame = frame, # sampling frame errors = cv, # precision constraints maxclusters = 10) # max number of strata to be evaluated # number of strata to be obtained in each domain in final solution: nstrat <- tapply(solutionKmean$suggestions, solutionKmean$domainvalue, FUN=function(x) length(unique(x))) nstrat # 1 2 3 4 5 6 7 # 10 10 7 10 10 8 10 # Optimization step ------------------------------------------------------------------------ solution <- optimStrata(method = "continuous", # method framesamp = frame, # sampling frame errors = cv, # precision constraints nStrata = nstrat, # strata to be obtained in the final stratification iter = 50, # number of iterations pops = 10) # number of stratifications evaluated at each iteration # Input data have been checked and are compliant with requirements # # *** Starting parallel optimization for 7 domains using 5 cores # |++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=19s # # *** Sample size : 209 # *** Number of strata : 55 # --------------------------- strataStructure <- summaryStrata(solution$framenew, solution$aggr_strata) head(strataStructure) # Domain Stratum Population Allocation SamplingRate Lower_X1 Upper_X1 Lower_X2 Upper_X2 # 1 1 1 318 9 0.027928 27 1048 32 1166 # 2 1 2 91 7 0.077012 99 7516 48 1202 # 3 1 3 82 8 0.091802 95 8114 436 2635 # 4 1 4 26 3 0.125069 286 29559 219 2792 # 5 1 5 49 9 0.176848 130 22454 2864 7093 # 6 1 6 8 2 0.250000 78 6261 8460 9082 # Sample selection -------------------------------------------------------------------------- s <- selectSample(frame = solution$framenew, # frame with the indication of optimized strata outstrata = solution$aggr_strata) # optimized strata with sampling units allocation # *** Sample has been drawn successfully *** # 209 units have been selected from 55 strata # # ==> There have been 8 take-all strata # from which have been selected 11 units head(s) # DOMAINVALUE STRATO ID X1 X2 Y1 Y2 LABEL WEIGHTS FPC # 1 1 1 5432 439 497 230 11 1 35.33333 0.02830189 # 2 1 1 5928 87 235 47 5 1 35.33333 0.02830189 # 3 1 1 5785 412 794 335 20 1 35.33333 0.02830189 # 4 1 1 5608 300 137 13 9 1 35.33333 0.02830189 # 5 1 1 5652 560 306 54 8 1 35.33333 0.02830189 # 6 1 1 5462 339 237 55 19 1 35.33333 0.02830189
