sampling (version 2.9)

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

Till<e9>, Y. (2006), Sampling Algorithms, Springer. Chauvet, G. and Till<e9>, Y. (2006). A fast algorithm of balanced sampling. Computational Statistics, 21/1:53--62. Chauvet, G. and Till<e9>, Y. (2005). New SAS macros for balanced sampling. In INSEE, editor, Journ<e9>es de M<e9>thodologie Statistique, Paris. Deville, J.-C. and Till<e9>, Y. (2004). Efficient balanced sampling: the cube method. Biometrika, 91:893--912. Deville, J.-C. and Till<e9>, Y. (2005). Variance approximation under balanced sampling. Journal of Statistical Planning and Inference, 128/2:411--425.

See Also

landingcube, fastflightcube

Examples

# NOT RUN {
############
## 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,
# simulation and comparison of the variance with
# unequal probability sampling of fixed sample size.
############
data(MU284)
# Computation of the inclusion probabilities
pik=inclusionprobabilities(MU284$P75,50)
# Definition of the matrix of balancing variables
X=cbind(MU284$P75,MU284$CS82,MU284$SS82,MU284$S82,MU284$ME84,MU284$REV84)
# Computation of the Horvitz-Thompson estimator for a balanced sample
s=samplecube(X,pik,1,FALSE)
HTestimator(MU284$RMT85[s==1],pik[s==1])
# Computation of the Horvitz-Thompson estimator for an unequal probability sample
s=samplecube(matrix(pik),pik,1,FALSE)
HTestimator(MU284$RMT85[s==1],pik[s==1])
# simulations; for a better accuracy, increase the value of 'sim'
sim=5
res1=rep(0,times=sim)
res2=rep(0,times=sim)
for(i in 1:sim)
{
cat("Simulation number ",i,"\n")
s=samplecube(X,pik,1,FALSE)
res1[i]=HTestimator(MU284$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)
# }