ratioest_strata {sampling}

Ratio estimator for a stratified design

Description

Computes the ratio estimator of the population total for a stratified design. The ratio estimator of a total is the sum of ratio estimator in each stratum.

Usage

ratioest_strata(y,x,TX_strata,pik,strata,description=FALSE)

Arguments

y

vector of the variable of interest; its length is equal to n, the sample size.

x

vector of auxiliary information; its length is equal to n, the sample size.

TX_strata

vector of population x-total in each stratum; its length is equal to the number of strata.

pik

vector of the first-order inclusion probabilities; its length is equal to n, the sample size.

strata

vector of size n, with elements indicating the unit stratum.

description

if TRUE, the ratio estimator in each stratum is printed; by default, it is FALSE.

Value

The function returns the value of the ratio estimator.

See Also

ratioest

Examples

###########
# Example 1
###########
# uses MU284 data as population with the 'REG' variable for stratification
data(MU284)
# there are 3 outliers which are deleted from the population
MU281=MU284[MU284$RMT85<=3000,]
attach(MU281)
# computes the inclusion probabilities using the variable P85
# sample size 120
pik=inclusionprobabilities(P85,120)
# defines the variable of interest
y=RMT85
# defines the auxiliary information
x=CS82
# computes the population stratum sizes
table(REG)
# not run
# 1  2  3  4  5  6  7  8 
# 24 48 32 37 55 41 15 29 
# a sample is drawn in each region
# the sample stratum sizes are given by size=c(4,10,8,4,6,4,6,7)
s=strata(MU281,c("REG"),size=c(4,10,8,4,6,4,6,7), method="systematic",pik=P85)
# extracts the observed data
MU281sample=getdata(MU281,s)
# computes the population x-totals in each stratum
TX_strata=as.vector(tapply(CS82,list(REG),FUN=sum))
# computes the ratio estimator
ratioest_strata(MU281sample$RMT85,MU281sample$CS82,TX_strata,
MU281sample$Prob,MU281sample$Stratum)
detach(MU281)
###########
# Example 2
###########
# this is an artificial example (see Example 1 in the 'strata' function)
# there are 4 columns: state, region, income and aux
# 'income' is the variable of interest, and 'aux' is the auxiliary information 
# which is correlated to the income
data=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),matrix(rep("sc",70),70,1,byrow=TRUE))
data=cbind.data.frame(data,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)),
1000*runif(235))
names(data)=c("state","region","income")
attach(data)
aux=income+rnorm(length(income),0,1)
data=cbind.data.frame(data,aux)
# computes the population stratum sizes
table(data$region,data$state)
# not run
#     nc  sc
#  1 100  30
#  2  50  40
#  3  15   0
# there are 5 cells with non-zero values; one draws 5 samples (1 sample in each stratum)
# the sample stratum sizes are 10,5,10,4,6, respectively
# the method is 'srswor' (equal probability, without replacement)
s=strata(data,c("region","state"),size=c(10,5,10,4,6), method="srswor")
# extracts the observed data
xx=getdata(data,s)
# computes the population x-total for each stratum
TX_strata=na.omit(as.vector(tapply(aux,list(region,state),FUN=sum)))
# computes the ratio estimator 
ratioest_strata(xx$income,xx$aux,TX_strata,xx$Prob,xx$Stratum,description=TRUE)