sampling (version 2.10)

samplecube: Sample cube method

Description

Selects a balanced sample (a vector of 0 and 1) or an almost balanced sample. Firstly, the flight phase is applied. Next, if needed, the landing phase is applied on the result of the flight phase.

Usage

samplecube(X,pik,order=1,comment=TRUE,method=1)

Arguments

X

matrix of auxiliary variables on which the sample must be balanced.

pik

vector of inclusion probabilities.

order

1, the data are randomly arranged,
2, no change in data order,
3, the data are sorted in decreasing order.

comment

a comment is written during the execution if comment is TRUE.

method

1, for a landing phase by linear programming,
2, for a landing phase by suppression of variables.

References

Tillé, Y. (2006), Sampling Algorithms, Springer.
Chauvet, G. and Tillé, Y. (2006). A fast algorithm of balanced sampling. Computational Statistics, 21/1:53--62.
Chauvet, G. and Tillé, Y. (2005). New SAS macros for balanced sampling. In INSEE, editor, Journées de Méthodologie Statistique, Paris.
Deville, J.-C. and Tillé, Y. (2004). Efficient balanced sampling: the cube method. Biometrika, 91:893--912.
Deville, J.-C. and Tillé, Y. (2005). Variance approximation under balanced sampling. Journal of Statistical Planning and Inference, 128/2:411--425.

See Also

landingcube, fastflightcube

Examples

############
## Example 1
############
# matrix of balancing variables
X=cbind(c(1,1,1,1,1,1,1,1,1),c(1.1,2.2,3.1,4.2,5.1,6.3,7.1,8.1,9.1))
# vector of inclusion probabilities
# the sample size is 3.
pik=c(1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3)
# selection of the sample
s=samplecube(X,pik,order=1,comment=TRUE)
# The selected sample
(1:length(pik))[s==1]
############
## Example 2
############
# 2 strata and 2 auxiliary variables
# we verify the values of the inclusion probabilities by simulations
X=rbind(c(1,0,1,2),c(1,0,2,5),c(1,0,3,7),c(1,0,4,9),
c(1,0,5,1),c(1,0,6,5),c(1,0,7,7),c(1,0,8,6),c(1,0,9,9),
c(1,0,10,3),c(0,1,11,3),c(0,1,12,2),c(0,1,13,3),
c(0,1,14,6),c(0,1,15,8),c(0,1,16,9),c(0,1,17,1),
c(0,1,18,2),c(0,1,19,3),c(0,1,20,4))
pik=rep(1/2,times=20)
ppp=rep(0,times=20)
sim=10 #for accurate results increase this value
for(i in (1:sim))
	ppp=ppp+samplecube(X,pik,1,FALSE) 
ppp=ppp/sim
print(ppp)
print(pik)
############
## Example 3
############
# unequal probability sampling by cube method
# one auxiliary variable equal to the inclusion probability
N=100
pik=runif(N)
pikfin=samplecube(array(pik,c(N,1)),pik,1,TRUE)
############ 
## Example 4
############
# p auxiliary variables generated randomly
N=100
p=7
x=rnorm(N*p,10,3)
# random inclusion probabilities 
pik= runif(N)
X=array(x,c(N,p))
X=cbind(cbind(X,rep(1,times=N)),pik)
pikfin=samplecube(X,pik,1,TRUE)
############ 
## Example 5
############
# strata and an auxiliary variable
N=100
a=rep(1,times=N)
b=rep(0,times=N)
V1=c(a,b,b)
V2=c(b,a,b)
V3=c(b,b,a)
X=cbind(V1,V2,V3)
pik=rep(2/10,times=3*N)
pikfin=samplecube(X,pik,1,TRUE)
############
## Example 6
############
# Selection of a balanced sample using the MU284 population,
# Monte Carlo simulation and variance comparison with
# unequal probability sampling of fixed sample size.
############
data(MU284)
# inclusion probabilities, sample size 50
pik=inclusionprobabilities(MU284$P75,50)
# matrix of balancing variables
X=cbind(MU284$P75,MU284$CS82,MU284$SS82,MU284$S82,MU284$ME84,MU284$REV84)
# Horvitz-Thompson estimator for a balanced sample
s=samplecube(X,pik,1,FALSE)
HTestimator(MU284$RMT85[s==1],pik[s==1])
# Horvitz-Thompson estimator for an unequal probability sample
s=samplecube(matrix(pik),pik,1,FALSE)
HTestimator(MU284$RMT85[s==1],pik[s==1])
# Monte Carlo simulation; for a better accuracy, increase the value 'sim'
sim=5
res1=rep(0,times=sim)
res2=rep(0,times=sim)
for(i in 1:sim)
{
cat("Simulation number ",i,"\n")
s=samplecube(X,pik,1,FALSE)
res1[i]=HTestimator(MU284$RMT85[s==1],pik[s==1])
s=samplecube(matrix(pik),pik,1,FALSE)
res2[i]=HTestimator(MU284$RMT85[s==1],pik[s==1])
}
# summary and boxplots
summary(res1)
summary(res2)
ss=cbind(res1,res2)
colnames(ss) = c("balanced sampling","uneq prob sampling")
boxplot(data.frame(ss), las=1)