UPtille {sampling} | R Documentation |
Use Tillé method to select a sample of units (unequal probabilities, without replacement, fixed sample size).
UPtille(pik,eps=0.000005)
pik |
vector of prescribed inclusion probabilities. |
eps |
the control value, by default equal to 0.000005. |
Return a vector (0 and 1) of size N, where N is the population size. 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 UPtille(pik) ############ ## Example 2 ############ # Selection of samples of municipalities # with equal or unequal probabilities. # Comparison of the accuracy by a boxplot. b=data(belgianmunicipalities) pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) N=length(pik) n=sum(pik) sim=10 ss=array(0,c(sim,9)) # the interest variable y=belgianmunicipalities$TaxableIncome # simulation and computation of the Horvitz-Thompson estimator for(i in 1:sim) { cat("Step ",i,"\n") ss[i,]=ss[i,]+c( c(crossprod(y,UPpoisson(pik)/pik)), c(crossprod(y,UPrandomsystematic(pik)/pik)), c(crossprod(y,UPrandompivotal(pik)/pik)), c(crossprod(y,UPtille(pik)/pik)), c(crossprod(y,UPmidzuno(pik)/pik)), c(crossprod(y,UPsystematic(pik)/pik)), c(crossprod(y,UPpivotal(pik)/pik)), c(crossprod(y,UPmultinomial(pik)/pik)) , c(crossprod(y,srswor(n,N)*N/n))) } # boxplot of the estimators colnames(ss) <- c("poisson","rsyst","rpivotal","tille","midzuno","syst","pivotal","multinom","srswor") boxplot(data.frame(ss), las=3) # The results of the simulations can be interpreted. # Simple random sampling, multinomial sampling, # and Poisson sampling are not accurate. # All the methods of unequal probability sampling seem # to have the same accuracy, except systematic sampling and pivotal sampling # that have variances which depend on the order of the file.