UPtille {sampling} | R Documentation |
Uses the Tillé method to select a sample of units (unequal probabilities, without replacement, fixed sample size).
UPtille(pik,eps=1e-6)
pik |
the vector of the prescribed inclusion probabilities. |
eps |
the control value, by default equal to 1e-6. |
Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value eps is used to control pik (pik>eps & pik < 1-eps).
Tillé, Y. (1996), An elimination procedure of unequal probability sampling without
replacement, Biometrika, 83:238-241.
Deville, J.-C. and Tillé, Y. (1998),
Unequal probability sampling without replacement through a splitting method,
Biometrika, 85:89-101.
############ ## Example 1 ############ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #select a sample s=UPtille(pik) #the sample is (1:length(pik))[s==1] ############ ## Example 2 ############ # Selection of samples of municipalities # with equal or unequal probabilities. # Comparison of the accuracy by boxplots. b=data(belgianmunicipalities) pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) N=length(pik) n=sum(pik) #number of simulations; for an accurate result, increase this value sim=10 ss=array(0,c(sim,8)) # the interest variable y=belgianmunicipalities$TaxableIncome # simulation and computation of the Horvitz-Thompson estimator for(i in 1:sim) { cat("Step ",i,"\n") ss[i,]=ss[i,]+c( HTestimator(y,pik,UPpoisson(pik)), HTestimator(y,pik,UPrandomsystematic(pik)), HTestimator(y,pik,UPrandompivotal(pik)), HTestimator(y,pik,UPtille(pik)), HTestimator(y,pik,UPmidzuno(pik)), HTestimator(y,pik,UPsystematic(pik)), HTestimator(y,pik,UPpivotal(pik)), HTestimator(y,rep(n/N,N),srswor(n,N))) } # boxplots of the estimators colnames(ss) <- c("poisson","rsyst","rpivotal","tille","midzuno","syst","pivotal","srswor") boxplot(data.frame(ss), las=3) # The results of the simulations can be interpreted. # Simple random sampling # and Poisson sampling are not accurate. # All unequal probability sampling methods seem # to have the same accuracy, except systematic sampling and pivotal sampling # that have variances which depend on the order of the units in the file.